Want to conquer negative numbers in binary? This fun, beginner-friendly tutorial breaks down two’s complement with step-by-step examples (-109, -29) and shows how to convert, pad, and subtract in binary. Learn sign bits, carry bits, and avoid common mistakes. Subscribe for more coding tips and tech tutorials that make learning a blast! Scan the QR code for more resources and join our community!

Introduction to Two’s Complement 00:00:00
Signed vs. Unsigned Integers 00:00:28
Sign Bit Explanation 00:01:55
Positive and Negative Representation 00:02:06
Range of Signed Integers 00:02:48
Padding Signed Integers 00:05:36
Converting to Negative (Example: -109) 00:07:00
Binary Addition and Carry Bits 00:10:16
Correcting Conversion Mistakes 00:16:38
Converting Negative 29 00:13:32
Subtraction Using Two’s Complement 00:18:21
Adding Binary Numbers (109 – 29) 00:20:41
Verifying Results 00:23:56
Conclusion and Call to Action 00:25:40

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Hey there! Let’s talk about representing negative numbers in binary.

We’re going to use a system called 2’s complement which is going to allow us to represent signed integers,

which means there will be a positive sign or a negative sign on the integer

and we’ll still be able to do it in pure binary.

So let me talk a little bit about what I mean first here.

signed and unsigned okay so if i just type the number 14 by itself that is uh that’s an unsigned

integer we don’t really know if it’s positive or negative like do we know that it’s negative 14 or

do we know that it’s positive 14 right so the sign is what lets us know if something is positive or

negative okay so if i if i type a number in binary let’s just do a pure binary number one two three

if you know how to convert binary to decimal you probably recognize right away that this is just

the number zero even if we add a couple of bits here that’s just like the number three

and so this is the number three but so far if if you haven’t learned signed integers in twos

complement or in binary then you don’t really know that there’s a sign you just kind of assume

that the number is positive by default if you’re not using twos complement and you’re just saying

and you’re just saying like well let’s just do a bunch of binary you know digits then yeah it’s a

safe assumption that the the sign is positive but we’ll use two’s complement which starts with the

idea that the highest bit the leftmost bit the bit with the height you know the most power that’s

going to turn into the sign that’s that’s going to turn into the plus or the minus so like you

the sign.

So this means that we have to decide, you know, does a zero mean positive or does it

mean negative or what means what?

So in two’s complement, we’ll say that zero is positive and one is negative.

So you can see right here that we’re still actually representing the number three, but

it’s positive three for sure because this sign bit right here is zero.

That’s positive.

Once we decide to represent two’s complement, then we can say that for sure.

On the other hand, if we put a one here,

then we definitely know that this number is now negative.

However, we don’t actually know that it’s a three

because the numbers don’t work out the same anymore

in two’s complement.

So the positive numbers, they will mostly look the same.

The negative numbers, they’ll look a lot different,

but they’ll still be valid in order,

you know, in terms of us being able to add them together,

subtract them from each other and things like that.

So two’s complement is pretty cool.

Let’s do, let’s see, what else can I tell you?

Oh, one thing to understand is that

One thing to understand is that in an 8-bit unsigned integer in binary, let’s say 1, 2,

3, 4, 5, 6, 7, 8, let’s say unsigned bits, maybe I’ll just put like, maybe just some

like V for value, all the bits are values, that means the range is 0 to 255 with 256

total combinations.

But if we want to use a signed number, then we’ll actually have the signed bit be the first bit,

and all the rest will be value bits.

1, 2, 3, 4, 5, 6, 7.

In this case, the range kind of goes down.

Because if you think about it, every single bit, you know, represents like, you know,

it helps towards the highest possible value that you can represent.

If we’re using the leftmost bit, then for an 8-bit integer, that’s 128.

integer that’s 128 that’s a value of 128 so we lose a lot off of the maximum

integer that we can represent so the range here is I think it’s negative 20

128 to positive 127 just keep in mind you’ll have to trust me in terms of why

is the negative 128 bigger and the positive 127 you know smaller but that’s

just the way it is so that means we only get these value bits here and if you if

that um let’s see if i can do this quickly enough without screwing it up we’ll say 127 minus um

minus negative 128 i guess that’s 255 and then also a zero but uh in terms of positive and

negative the way this is going to work out is the zero will probably show up twice because uh

255 possible combinations with seven bits.

Normally you would have a range from negative, sorry, from zero to positive 255.

And in this case, we’re just, you know, losing our range, but we can represent negative numbers.

Anyway. Okay.

So let’s talk about doing an example real fast. Let’s see.

I’ve got like a little notes to tell me what I should do. Okay.

It’s important to understand that normally when you have, let’s say, let’s say you have

like an 8-bit number and you go 1, 2, 3, 4, 5, 6, 7, 8.

And then you have 2 bits right there and so this is like, you know, positive 3.

If you wanted to copy that number into more bytes, like for example, if you wanted to

take a 2-byte integer and have it copy the value of a 1-byte integer, then it’s pretty

easy.

zeros to the left you’ll say one two three four five six seven eight that would work perfectly

however if you did this with a negative number let’s say that we have a negative number

I’m going to put some of the random patterns so that you don’t think it’s the three let’s see

one two three four five six seven eight that’s eight total so I’m going to make that a one and

then get rid of that so we have like eight negative number if we were going to copy that

integer then we would copy paste it to start but then you’d have to pad with

ones to the left one two three four five six seven eight same negative number

more bits so be very careful about how you pad if you’re padding an unsigned

integer then yeah you’ll always pad zeros to the left no matter what is

happening but if you’re padding a signed integer then you have to pad differently

signed integer you have to pad with whatever the highest bit is so in this case the highest bit was

a zero so we do pad with zeros but then in this case the highest bit was a one so we have to pad

with ones if you don’t do that you’re going to end up with a number that doesn’t actually make

sense okay so now let’s work on actually converting a number to a negative number or representing a

negative number in twos compliment okay so i’m going to write twos compliment here and then uh

Let’s start off with the number negative 109.

Okay, how do we do this?

The first thing is convert it to its positive form.

Take the absolute value. Okay.

So we’re really just, you know, take positive form here,

and that’s just going to be positive 109.

Okay, no problem.

I’ll say start with negative 109, and then we’ll take the positive form 109.

Now we’ll convert it to binary.

Okay, this is not a video that teaches you how to convert to binary, so I’m just going

to try to do this in my head real fast here.

It’s going to be, let’s see, we got 8 bits, we’ll use just 8 bits to store the number,

and because it’s low enough and I don’t want to use that many bits, so it’s odd, so I can

add a 1 there, but maybe for now I should find the highest bit that is less than the

actual number.

So this is the 128 bit right here. So that’s going to be a zero. This is the 64 bits

I’m going to put a one there and I’m just going to say

Mmm, maybe like

This is like maybe not the smartest way to do it. I’ll say 109 minus 64

Because I put a one there and then 45 so now this is 32 that’s less than 45. So I’ll put a one there and

Then it’s going to be minus 40

So it goes from 45 to 13.

So then that was the 32.

Okay, so 128, 64, 32, and then 16.

Is 16 less than 13?

No, it’s not.

So we’ll put a zero here.

And then the next one is going to be just four.

Four is definitely less.

So I’ll put a one bit there.

And then I’ll subtract four.

And then one, two, four.

Oh, wait a minute.

One, two, four, eight.

wait a minute one two four eight sorry that was supposed to be subtracted uh subtracting eight

because that was the eight bit uh then i want to get five so here is the four bit so i put a one

there and then i’ll just put a one here because four plus five is equal to uh i’m sorry four plus

one is equal to five so let’s see um it is let me just double check here one

one let me just double check my conversion real fast it’s going to be

the one bit plus two four plus eight six thirty two plus thirty two plus sixty

four did I get one on nine yeah okay so I guess I did it right so convert to

binary and that’s going to be this the next thing we’ll do is we will invert the

bits I made a little edit jump here because I inverted the bits incorrectly

on the first try which is sad but hey it happens the next thing we’ll do is

but hey it happens the next thing we’ll do is we’ll invert the bits so basically you know we

take this original sequence here and i’ll just turn every single bit uh i’ll flip it i’ll flip

ones to zeros and zeros to ones so i’m going to go one zero zero one zero zero one zero okay so now

we have this number invert the bits then we just have to add one so we’ll add positive one to that

that it’s just going to be a one there at the end.

But sometimes that might not be the case

because what if we already had a one there

and we had to add one to that?

Well, we’d add one to the right side

and it would turn into a zero

and then it would carry a bit to the left.

That would become a zero

and then the carry bit would show up all the way over there.

So I just want you to be aware of the fact that

when you add two binary numbers together,

you have to be careful.

You have to add them the same way you would add decimal numbers.

For each digit’s position,

you have to add the two numbers together and then if they overflow then you just

kind of wrap around to the lowest number again subtracting you know the highest

value or sorry subtracting the base like in decimal if you add 9 and 9 the answer

is 18 but you’re not going to write 18 in that one position you’re going to

subtract the base which is 10 so it’ll actually be 8 and then you’ll carry the

plus nine is equal to eight carry the one right so we’ll do the same thing in binary we’ll say

if we ever get a one plus one when we’re adding the answer will be two but then we subtract the

base which is two so the answer is actually zero carry a one bit keep that in mind i’m just gonna

write it all out for you so you can kind of get a little bit of practice it’s important to to

practice this because it’s easy to get wrong i’m going to put a bunch of dashes up at the top to

and I’m going to say we’re going to add, you know, one number plus another number,

put a little plus symbol over there just to try and make sure we do it the right way.

Okay, so how do we add these?

Well, we’ll just go to the right side.

Zero plus one is one, no carry bit.

One plus zero is one, no carry bit.

Then we got a couple zeros here, no carry bit, of course.

One plus zero is one, no carry bit.

And then a couple zeros and then another one with no carry bit.

Okay, so, you know, we could have done that pretty easily, but

but well now we’re getting a taste for binary addition that might be harder later.

So we’ll just do that for now.

And now this is the two’s complement representation of negative 109.

I’ll say now we have negative 109 is equal to that.

leftmost number the most powerful sorry leftmost bit the most powerful bit is a one remember one

always indicates negative so when you’re looking at it if your leftmost bit turns out to be a zero

then you probably did something wrong or you had an overflow maybe um and again if we were going

to try to you know send this number into a two byte number or an eight byte number or whatever

uh then we would just have to pad with the sign bit so one two three four five six seven eight

help my brain so this was this is the way it would look in a two-byte number this is the way it would

look in a three-byte a four-byte and five six seven how many one two three four five six seven

okay one more this is what it would look like as an eight-byte number or a quad word 64-bit number

yeah okay so now we know how to do negative 109 okay so now let’s do a number that’s a little bit

negative 29. So let’s say convert, or how about represent negative 29 into

2’s complement. Okay. So first we, you know, first get the absolute value.

So just 29. And then we have to invert the, sorry, we have to get that into binary. So

next convert to binary. And I’m going to start with zeros, one, two, three, four, five, six,

1, 2, 3, 4, 5, 6, 7, 8.

For this video, remember, we’re choosing to use one byte integers.

But if you wanted to do a bigger one or you had to do a bigger one,

then just, you know, keep that in mind.

Okay, so 128 is not smaller than 29.

64 is not.

32 is not.

16 is, though.

So I’ll put a 16 bit there.

And I’ll just subtract 16 from 29.

29 minus 16.

Now we’ve got 13 left.

So 64, 32, 16.

six four thirty two sixteen eight okay so now I’m gonna put a one bit there and

I’m gonna subtract 8 from the remainder and then we got a five which is pretty

easy to do eight four and then a one so now we have well zero zero zero one one

one zero one that’s the binary number the positive or unsigned representation

representation. So now we’ll add one. Positive one. And let’s try to do this the right way so

that we can practice carry bits with addition a little bit. Notice how this one is already there

on the right side. So it’s going to, we’re going to have at least one carry bit for sure.

So then I’m going to go doop like that. And then I’m going to say that we have like, you know,

what is the result? Put a positive sign there. And then I’m going to put a bunch of dashes

my carry bits because I can I can forget that pretty easily. So the first thing is we add one

and one. The answer is two, but we can’t put the number two here because it’s binary. Instead we

need to subtract the base which is two. So two minus two is equal to zero, but then we have a

carry bit of one. So I’m going to put a one there. The first carry bit will stay as a dash for this

whole you know exercise because you’re not going to carry on to the first digit. So now we have

what would have been just zero plus zero now we have one plus zero plus zero so

that means this is going to be one and then the carry bit is just going to be

zero because we don’t actually carry anything so then we have zero plus one

plus zero so that’s going to be a one and then zero carry bit and then zero

one zero is just going to be one and then there’s going to be no carry bit

and then zero one zero again a one no carry bit because we didn’t actually

zero zero zero and then I’m just gonna put zeros here okay so now we have

successfully added I blew it totally blew it I always forget steps don’t

forget the steps this is a good lesson I’m gonna leave this in the video

because I want you to see that everybody makes mistakes and you got to practice

practice practice especially before you have to actually do this in real life or

or something like that.

Next, convert to binary.

Before you add one, I’m gonna just remove this.

Oh my gosh.

Next, flip the bits,

which is gonna be 1110010.

Okay.

So now we take this bit flipped number

and we will add one.

So that’s gonna be zero, zero, zero, zero, zero, zero, zero,

one, oh, it’s too easy.

Maybe I got excited and I thought,

excited and I thought, oh, it’s carry bit time.

But even though the last edition that I did was wrong because I forgot to carry

the or flip the bits, you still at least saw a little bit about how to carry the bits.

Right. OK, so it’s just going to be one.

Let me start from the right side.

One one zero zero zero one one one one one one.

Let me just double check here.

One one one zero zero zero.

OK, so I got that.

Now we have.

negative 29 in twos compliment. Again notice if we actually tried to add those numbers up to be

like an unsigned binary number they’re not really going to make sense because this is like 64 plus

32 plus 3. So what would that end up being? Let’s just double check here. 64 plus 32 plus 3, 99.

That’s not actually the number but the number is 29. So keep in mind you can’t just look at this

unless you’re like really, really practiced.

Okay, and again, notice that the number is 1 at the very left,

indicating that it’s a negative number.

Now, let’s look at how to subtract one number from another

using 2’s complement.

Okay, so what I want to do is I want to subtract,

let’s say, 29 from 109.

Okay, so let’s subtract, and I’ll just say 109 minus 29.

109 minus 29.

And how I would do that is basically I’ll start by just taking 109.

Let’s see, convert to binary.

So I’m just going to copy paste that number.

So 109 is this and then 29, take the positive version.

It is just, let’s see, before we flip the bits or anything,

let me make sure that I grab the right one.

Invert the bits, okay.

So positive 29 is this number.

Whoops.

is this number whoops let me put parentheses around that so it’s easy to tell and then I’ll

put a positive sign there like that maybe like that nope nope nope nope how about this okay

so now we have both of these numbers in positive form so now if we added 109 plus 29 that wouldn’t

negative positive 29 that would be what we wanted right because really if you’re subtracting

i’ll say aka

positive 29 plus negative 29 all we really need to do is um invert the 29 and then add the result

to 109 so that means we’ll we’ll turn positive 29 into negative 29 using two’s complement

through the steps again but basically put it there but basically you know that’s negative 29

so say positive 129 is equal to what i just put up here and then negative 29 is equal to

maybe i should do the parentheses again for clarity uh is equal to this okay so you can tell

that positive 29 is pretty pretty different from negative 29 but now we have

29 but now we have both of those numbers so let’s see 0 1 1 0 and then we’re ready to add okay all

we got to do is add them together next add them together maybe I should write the steps up here

negative 29 using twos complement and then next add them together so then I’m

going to copy paste the bits here and it’s going to be this plus this do a

positive plus sign just to remind ourselves that we are actually adding

and then I’m going to put a bunch of placeholders for sign bits up at the

top and now we’ll have a little bit more fun adding numbers together maybe I’ll

drag this down

Oh my god. Oh, there we go. Okay. So I’ll start with the one on the right, the position on the

right. That’s going to be one plus one equals two, but then that’s an overflow. So I’m going to

subtract the base. So it’s going to be zero. And then don’t forget to carry the one. Oh,

cool. More interesting. So we have one plus zero plus one. That’s going to be another two carry

two carry the one so it’s going to be zero and then carry the one again so i’m going to put the

carry bit up there and then again we have one plus one is equal to two so it’s going to be zero

carry the one again zero carry the one and then finally we don’t really have a carry bit

um so we’ll just have like a one and there’s there’s no carry so it’s going to be you know

carry a zero and then we add these two together so it’s going to be a zero carry the one and then

Now we have a three.

Oh, that’s kind of nice.

So this is an interesting edge case kind of.

One plus one plus one is three.

But if we subtract two, the base from it, you know, three minus two, it’s going to be one, not zero.

So it actually is going to be a one and then carry the one on top of that.

Then for here, let me space this over a little bit so that I can illustrate what’s going on a little bit better.

We’re going to have one plus zero plus one.

definitely going to be zero and then carry the one but there’s no bit where that carried one can

can show up on right so that one overflows it falls off the edge if this was a bigger number

then okay we you know if we had more bits to this number then sure we would just keep carrying over

over to the left but remember we said before that when we have a very big number let’s see

bits it’s just ones all the way to the side that will actually help us make sure that if our final

number is actually going to end up being positive that everything kind of like dominoes like carry

the one carry the one carry the one carry the one carry the one all the way until one of the ones

falls off think about it so anyway this one just is gone we don’t really care about it anymore

the result is going to be just only eight bits because that’s the number that we started with

bunch of zeros what is you know the final answer let’s just compute this

real fast to decimal so this is 128 and then 64 so it’s gonna be 64 plus not 32

but 16 so 64 plus 16 that’s gonna be oops 16 that’s gonna be 80 and now we

just have to ask ourselves again as like a final step to double check yourself to

what you’re doing and that you got it right is just punch up 109 minus 29 just to make sure

109 minus 29 whoops what happened here 109 minus

oh i think i stole my subtraction key for the annotator 109 minus 29 is 80

so again you know if you’re if you’re trying to like you know write something down to do some

you know taking an exam or something you definitely want to double check yourself in several ways

As you can tell from this video alone

I got one of these things wrong because I forgot to input the bits as a step before adding one

So you know your final step should be actually trying to add two numbers together or subtract numbers or whatever

You’re doing to make sure that you got the binary correct

So let’s see

Hmm

I guess maybe your first indication that the result was going to be positive would be that

there’s a zero there. And just, you know, as a sanity check, you look at the top and you’re like,

well, I was going to subtract a small number from a larger number. So the result should probably be

positive, right? Like 29 is like way lower than 109. So it should be positive, which means the

final result should have a zero at that leftmost position. Okay, so that’s two’s compliment,

two’s complement how to convert numbers from positive to negative in two’s complement you

know what the sign bit means and all that stuff and how to perform subtraction via two’s complement

i hope you enjoyed this video thank you for watching i hope you learned a little bit of

stuff and had a little bit of fun see you in the next video hey everybody thanks for watching this

video again from the bottom of my heart i really appreciate it i do hope you did learn something

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The post Master Two’s Complement: Convert & Subtract Negative Binary Numbers appeared first on NeuralLantern.com.

Hey there, Linux newbies! Ready to unlock the power of the Linux command line? In this fun and approachable guide, we dive into the Ubuntu terminal to teach you the essentials of command-line magic. Perfect for beginners, this video covers everything from launching a terminal (like the awesome Terminator emulator) to mastering commands like ls, cd, mkdir, and rm. You’ll learn how to navigate the file system, create and delete files, edit code with Nano (sorry, Vim fans!), and even compile C++ programs with GCC. Plus, we’ll show you how to install cool programs like GIMP using apt and wield sudo like a pro. Whether you’re switching from a GUI or just curious about the terminal’s hacker vibes, this video is your gateway to a whole new world of open-source tools. Stick around till the end for a quick peek at graphical editing and a heartfelt call to join our community! Hit that subscribe button, scan the QR code to check out more tutorials, and let’s keep exploring Linux together. Drop a comment with your favorite command or what you want to learn next! #Linux #CommandLine #Ubuntu

Introduction to Linux Command Line 00:00:00
Ubuntu Linux Terminal 00:00:04
Benefits of Terminal Usage 00:00:09
Desktop Environments (XFCE vs. GNOME) 00:01:07
Launching the Terminal 00:01:55
Terminal Emulator (Terminator) 00:02:06
Understanding the Shell (Bash) 00:04:00
Echo Command and Variables 00:04:06
Clear Command 00:07:34
Navigating File System (PWD) 00:08:21
Listing Directory Contents (LS) 00:08:56
Using Man Pages 00:10:37
Changing Directories (CD) 00:13:15
Creating Directories (MKDIR) 00:14:51
Going Up Directory Levels 00:15:57
Creating and Deleting Files (Touch, RM) 00:19:03
Editing Files with Nano 00:21:00
Editing Files with Vim 00:26:24
Installing Programs with APT 00:28:06
Using Sudo for Root Access 00:32:29
Updating and Upgrading System 00:34:54
Graphical File Editing 00:36:05
Compiling C++ Programs (GCC, G++) 00:39:53
Executing Programs 00:40:57
Conclusion and Subscription Call 00:43:04

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Hello there. Today I’d like to show you a little bit about the Linux command line

inside of a terminal. More specifically I’m going to be doing this on Ubuntu Linux.

This is great for beginners to start to get to know how to issue commands and do

things like that and if you’re used to doing everything in a GUI in a graphical

user interface then you probably have no idea how much fun it is to actually

work inside of a terminal. There are tons and tons of programs that you can gain

can gain access to once you start getting more comfortable with the terminal.

When you look around at the open source world and all the wonderful tools that people make,

you’ll find out pretty quickly that a lot of programmers just write tools that only

work with the command line.

And you know, maybe later if someone else comes along and wants to add a graphical

interface for it, then they do.

But lots of times that doesn’t actually ever happen.

And so you sort of open up a whole new world for yourself when you learn to use the terminal.

when you learn to use the terminal.

Anyway, and then you also look really cool like a hacker.

So I’m on a desktop engine called XFCE

or a desktop environment called XFCE.

Most new Linux users who are on Ubuntu

are probably looking at the GNOME desktop.

So let me just say real fast,

if you have a desktop that looks nothing like this

and you think you’re on GNOME because you just installed vanilla Ubuntu or something,

then you probably want to take a look at the top left corner of the screen

for a little button called Activities,

or at the bottom left of the screen for a button that I think is like nine dots.

Both of those buttons will allow you to search for programs on the system.

What you should do is basically click one of those buttons

and then start typing in the word Terminal

until you see a terminal pop up and then you can click on it

and then you can launch it.

and then you can, you can launch it. Okay. So for me though,

I already have this set up on my desktop.

So I’m going to click on my little terminal icon and I’m going to launch a

terminal. For those of you who don’t know what terminal I’m using right now,

this is called terminator. I think it’s really cool.

I’m personally a huge fan of this terminal. Uh,

the main reason is that it’s really easy and fast to split the panes.

So you can do multiple, uh, sessions.

If you’re connected to multiple remote machines at the same time, um,

machines at the same time, you know, later in your career. It’s really convenient. It’s actually

kind of broken right now a little bit, but not too bad. I still love it. Okay, so I open up a

terminal. Technically, this is called a terminal emulator. The real terminal would just be like a

completely black screen, and you wouldn’t be able to see anything else graphical. So this is sort of

like a windowed program that runs another program under the hood that helps this program talk with

talk with the operating system and it sort of performs two-way communication and shows you

what the operating system is saying to you and doing and things like that. So,

but for all intent and purpose, this is a, this is a terminal. I always call this a terminal.

Okay. Let’s see. Maybe I need to increase the font size real fast. Um,

I got a profiles out if I do mono space and I just do it like a little bit, a little bit bigger

bigger than the default so it’s easier to watch on a video. Okay how about that is that better?

I think that’s probably better. Okay so for starters uh you’re looking at a command line

interface you’re looking at a terminal this is a terminal emulator program uh we have like a

blinking cursor you can enter commands and stuff like that it’s important to understand at first

that um you’re actually already inside of a program remember I said that the terminal emulator is a

and it helps go between you and the operating system.

There’s also another program that sort of interprets the things that you’re saying

before sending that off to the operating system.

The program is different depending on what environment you’re using,

but in Ubuntu, it usually defaults to bash.

So I’m going to type a quick command.

We’ll explain what these commands do in a second.

And I’m going to type echo shell,

and that’s going to tell me what interpreter we’re using.

So by default, we’re using an interpreter called bash.

So if you hear anybody say, hey, I’m in bash or I got a bash script.

Well, this is what it is.

It’s a program that will be understood by bash.

Okay, so what did I just type?

I typed echo and then I typed a dollar sign and then I typed shell.

So on the terminal, you know, you can type any command you want.

It may not actually work, but you know, you can type.

The way that your command is usually interpreted is if you type just one thing,

then that’s considered the program that you want to execute.

the program that you want to execute so if i type the word echo by itself and hit enter

then bash or i’ll just say you know the shell or the terminal is going to look for a program named

echo and if it finds it it’ll execute it um there’s a there’s a special way that it searches

for programs like uh the the program echo for example it has to it has to go somewhere in the

operating system right there has to be a path so if you type which echo you can see exactly where

system so slash user slash bin slash echo so that’s where it is but i can just type echo by

itself because the system knows how to go search through special system paths looking for the echo

program that you typed so it can find the real location anyway so i type echo and this program

launches and it doesn’t really do anything the thing about the echo program is if you just type

actually receive what you typed after after the echo program executable name

and it’ll just print it back to you.

So what’s happening here is the bash interpreter, the shell,

it’ll always take the first argument.

We call these arguments, words or symbols separated by spaces.

The first argument is echo.

That’s considered the program that you want to run.

And every argument after that is actually just sent into the program that you launch.

thing that’s actually launching here is the echo program and then hello is a string that gets sent

into the echo program you can do as many arguments as you want actually i don’t know if there’s like

a huge limit huge limit you can probably type a lot of these before you run out and so i’ve typed

three arguments technically the echo program is is argument zero the first argument but um i’ve

typed out three arguments that will get sent into the echo program and you can see that echo received

three of them and just printed them out and that’s it so it’s the echo program is pretty simple but

if i if i type a dollar sign and i like actually let me just type shell by itself if i say echo

shell it just prints the word shell because that’s interpreted as just like a regular string but if i

put a dollar sign in front of it then bash considers that to be a variable and so what it’ll do is it’ll

go into memory wherever the variables are stored and it’ll try to find a variable named shell

variable named shell and if there is one it’ll take the value that’s inside of shell which in

this case is just you know bash and it’ll convert the symbol dollar sign shell into

the actual variable value and then it’ll print that it’ll send that into the echo command

so if i say echo shell step one it looks for variable name shell step two it grabs bin bash

and replaces that where the dollar sign shell was written and then it sends that into the echo program

into the echo program.

So now you know how to launch a program.

Here’s another program.

It’s called clear.

If you just type the, you know, the command clear, then a program called clear gets launched.

And all it does is just to help you clear the terminal.

If you want to keep things a little clean, just to prove to you that this is a program,

we can type which clear and notice how it actually has a path in your operating system.

User bin clear.

This will be different if you’re on a different operating system than mine, but it’s all okay.

It’s all okay.

All right.

So where am I?

Because you can see that I’m at some sort of a location.

It says Mike at lectures.

That sounds like the name of my computer and the name of my profile.

But where am I in the file system?

Because your computer is like, you know, a big file system.

There’s lots of files and folders all over the place.

Where is the terminal sitting?

Is it sitting anywhere in the file system?

It actually is.

It’s sitting in your home directory by default, unless you’ve made some customizations.

unless you’ve made some customizations, I can access the current working directory

by typing the command PWD, print working directory.

And again, this is a program and its whole job is just to print

where the working directory currently is.

So the working directory means where you’re currently at,

where you’re situated, where you’re looking at.

And it’s saying that I’m in my home folder.

In Linux, the home folders are usually slash home slash your username.

So if I want to see what’s inside of my home folder,

I can use another program called LS, which just lists the contents of a folder.

So I’m going to type LS and it tells me I’ve got all these folders,

desktop documents, downloads and so forth.

LS takes arguments.

Remember, we have arguments like if we did echo hello,

then it’ll print the word hello, but we can give the LS command some arguments too.

We can say LS, I’d like you to do, you know, some stuff.

So what do we want it to do?

Let’s make it print all the files and folders,

even those that might be hidden because they,

on Linux, if a file or folder starts with a period

in the name, it’ll usually be hidden by default.

So if we want to print everything, we can say dash a.

And if I want to print in a vertical list style,

I can put an L in front of there.

So I can say LS, which is the program

and then dash LA is the arguments I give it.

And that’s going to tell it to print my directory

with all hidden files and folders shown.

Notice how all this stuff showed up

that wasn’t there before,

like bash history.

I have a cache folder.

But then there was also some stuff

that was there before,

like the documents folder,

the music and the pictures folder,

and so forth.

So you saw these things before.

Like, let me just at least highlight one.

So you saw the videos folder there before.

You just didn’t see all those other hidden ones

because they had dots

in front of their file name.

in front of their file name or folder name depending on what they are okay and

then of course you can see that this is a vertical list and you’re getting a

little bit better now at giving arguments to programs so how did we know

that ls takes dash la as an argument or as some arguments you could search on

the internet which is pretty fast usually you can also use a program

called man the man program will give you information on another program most

programs have MAN entries so when you install the program there there will be

like a new manual page that shows up in the MAN program so I’m going to type MAN

LS and hit enter I’m basically going to launch the MAN program and I’m going to

tell it that I want information on the LS program so I hit enter and then it

sort of shows me like a big you know little instruction thing a little sheet

a little well it’s actually not little depending on the program this could be

tells you all the things that we can do with this program. So right here you can see the

dash LA part that we did earlier. Whoops, what did I do wrong? The dash LA part that we did earlier.

That’s the dash A. And we could also instead have just said dash dash all.

That’s what the manual is telling us. Where’s that dash L, the listing? Let’s see, it’s somewhere in

here. H I J K L, maybe I should do a page down.

Maybe I should do a page down.

Yeah, there we go.

So, well, there’s no dash dash list.

I was hoping that there would be a dash dash list,

but this tells you at least that you can say dash L to use a listing format.

And there’s tons of other options that you can learn and read about

if you just take some time to explore the man page.

Kind of cool, right?

Okay, so how do you get out of this?

By the way, how do you search for stuff?

I’m going to search by using the slash key.

key so like you know the the web slash key I’m gonna hit slash and then I’m

gonna type something I’m gonna say maybe block and then hit enter and notice how

it highlights on the first match I can do a regular end to go down to the next

match or I can do shift in like a capital N to go backwards up to the

previous match so this helps you you know kind of search through man pages and

things like that and the cool thing about what the man page is using right

It’s using a way to display itself.

I think it’s either using a program called less or it’s using a program that works very

similarly to a program called less.

So the program less, it’s just, it loads up a document for you and it lets you do things

like this, scroll up and down, search for things, go to a line number, you know, and

just, you know, it’s, it’s, it’s very convenient, right?

Like it pages in the terminal.

If you want to exit this, you just got to hit Q.

So I hit Q right now.

So I’m going to do man LS again, hit Q, and then I get out.

So now we know a few commands.

We know how to see where we’re at in the file system and list directories and things like that.

Let’s go into the documents directory with a special command called CD.

So CD stands for change directory.

And if I just say documents and hit enter, now the shell itself is inside of a different folder.

It was in my home folder before.

Now it’s in my documents folder.

If you’re ever unsure of where you are, use the PWD command again to figure out what’s going on.

Okay. Oh, look, I am inside of my documents folder.

If you ever find yourself in some sort of a deep, deep subfolder, let’s see.

I don’t even let’s do like user live live.

LiveX32.

Oops.

What am I doing?

There we go.

What about this library?

I’m just going into a random folder right now just to show you that we can go pretty

deep.

So I think that I’ve reached the end of that.

Okay.

So suppose I’m navigating around and I’m in some, some kind of a folder and I’m at,

I do PWD and it says, oh no, you’re like way deep in some other folder.

How do I get back to my home folder?

Well, you could type out the whole home folder if you wanted to, but the easiest way to get

pwd with no arguments.

Once you hit enter, it’ll drop back down to your home folder.

And if you’re not sure, then use the pwd command.

Okay, so we’re doing pretty well.

We’re kind of like navigating in here.

Let’s make a directory.

I’m going to go into my documents folder again.

And let’s see.

So right here I’ve got like, whoops, I’ve got some documents.

Let me make a directory called temp with the command make directory.

so uh well mkdir is the name of the program the first argument i gave it was temp and so it just

created a folder for me called temp so if i say cd temp i can now go into the folder that i just

created if i list the contents of that directory again it’s empty because i just made it pwd lets

me know where i am just to make sure when you’re new to the terminal you actually i still use this

customize my terminal so it doesn’t print the full the full path there it just prints the current

directory name so i kind of get lost sometimes so you just use the pwd command to figure out where

you are and by the way just as a reminder we could always do man and the name of a program so i’m

going to say man make dir and there’s options even for making a directory i’m not going to go over

those but just to let you know there’s a lot to explore okay so now i’m inside of the temp directory

I’ve made a folder. What if I want to go one level up? What if I don’t exactly want to drop

to the home directory, but maybe I went one level too deep and I want to go back up one level.

Well, again, I could type out the whole thing. I could say go home and I could say documents

and whatever. But by the way, I’m hitting control C when you see that care at C that usually tries

to get the current program to stop. But when you’re inside of bash, it’ll just sort of like

abort the current command and go to another line.

Okay, so how do I go up one level?

Well, in Linux, there are two special directories

that have periods in the name, well, they are periods.

The directory known as period,

actually, let me show you the full,

yeah, okay, well, the empty directory listing,

notice how it actually does show me two things.

It doesn’t show me nothing,

it shows me these two directories right here,

that’s not a mistake.

So this directory, the one with just one period, that always represents the current directory

that you’re in.

So if I use just a period to go into a directory or to do something to a directory, that period

will represent something different based on where I am.

Am I in my home folder?

Am I in the desktop?

Am I somewhere else?

The period changes based on where you are.

dot it always means i’m getting used to this new pen setup it always means it always means there we

go it looks like a emo guy with his hair like to the side um it always means the parent directory

so remember before we could type we could type cd and then some directory name right to go into a

directory uh now we can type cd dot dot and that’s basically saying we would like to change directories

change directories, we would like to go to the documents directory.

Why?

Because the documents directory is the parent directory of the temp directory.

So if I say cd dot dot, notice how it goes up one level.

Let’s do that again just to be sure.

So I’m going to say pwd, and if I say cd dot dot, and then pwd again,

notice how we were in temp, and as soon as we went up one level,

it went to documents.

So it’s just kind of a quick way.

you know, use a bunch of directory names separated by slashes.

You can also put dot dot in any directory that you want.

So like imagine I’m in the temp directory again.

I could say let’s go up one directory and then a slash and then up another directory

and then a slash and then up another directory.

And I should end up in the home folder.

Isn’t that kind of funny, right?

So I’m saying like give me the parent directory of the current directory

and then give me its parent directory and then give me its parent directory.

So I went up three levels.

its parent directory. So I went up three levels.

So let me drop to my home folder and go back into documents and go back into

temp. Whoops.

I forgot to do CD.

Now we’re getting pretty good at navigating. Let me make another directory.

I’ll call it delete me because I intend to delete this directory.

There’s a program called RM remove that lets you delete stuff.

Actually first, before we delete that, let’s use a program called touch.

and the program touch just sort of like creates a blank file.

I think if the file already exists, it won’t mess with the contents,

but let’s do an experiment in a moment.

So I’m going to say touch blank file.

It should create a file for me called blank file.

So now I’ve got a directory and a file called blank file.

Now I can remove the blank file with the RM command.

So just RM and then give it the name of the file.

Be careful with RM.

He’ll destroy your file system if you’re not careful.

and now let’s remove the delete me folder when you try to remove folders you have to tell the

remove command that you intend to delete a folder by specifying also the dash r command which means

this is a folder i would like you to recursively delete it so let me just type it without that

real fast and it says hey i can’t do it it’s a directory so i’m going to say all right now

And it did it.

Some other useful flags you might want in the future.

The first one that I like is V for Verbo.

So it’ll print everything that it deletes.

And F for Force.

If you’re absolutely sure that you know exactly what you’re about to delete,

then Force will make it so that this program won’t start asking you,

are you sure? Are you sure? Are you sure?

So it’s kind of dangerous, but it’s also pretty convenient.

Imagine that.

Anyway, so let’s see what else can I when I talk about here, we know how to like touch to create a blank file and create a folder and navigate all around. Let’s edit a file. Let’s actually edit a file in the terminal. So there’s kind of like an age old argument between the Vim people, or the V people, and the nano people. And so I just want to say that if you were a Vim person, don’t ever talk to me again for the rest of your life.

again for the rest of your life just kidding you’re okay we can sort of be

friends but I’m personally a nano person so what am I talking about nano is just

another program it may or may not be on your system I think on a boon to it

should be there by default let me just double check yeah it should be there by

default we’ll talk about how to install programs in a second I’ll go sudo apt

install just to remind myself but so you type nano to execute the nano program

of a file that you want to edit.

So let’s edit a file called my program.

Whoops, program.cpp, just if you’re writing some code.

And this tells the nano program that you would like

to edit this file named my program.cpp.

You hit enter and you have like a nice little editor

that shows up.

Notice at the bottom,

you have a bunch of little shortcuts, right?

So if you do, actually let’s look at this one

Actually, let’s look at this one over here first.

If you hit control O, that means save the file, write it out.

If you hit control X, that means you’d like to exit the editor.

So if I want to get rid of the editor and just like, you know, go back to the terminal,

the normal command line, I’ll do control X.

There’s a bunch of other stuff you can do.

And there’s like a big help menu.

alt n to see line numbers in nano so that makes it a lot more convenient for coding so i’m going

to do alt n to get those lines off let me just type the word hello real fast hello

okay so now i want to save this let’s do uh we can do control o to just save it but we’ll stay

inside of the editor or we can do control x to save it and then exit the editor so i think i’m

going to exit them say control x notice how at the bottom it asks me do i want to save the modified

That just means I’ve been editing inside of this like, you know, temporary area.

Do I want to actually save it?

So I’m going to hit Y for yes.

Then it asks me, you know, what’s the name of the file that you want to save?

Well, since I specified my program when I launched Nano, it already knows what I want to do.

If you didn’t specify the name of a file, then you could provide it here.

So I’m just going to hit enter.

And now the program exits.

If I list the contents of the directory, I can see that I now have

the world’s worst C++ program ever because it’s just hello that’s not going

to compile so how do I see the contents of a file with the terminal well for

starters obviously you could just type the name of the program again for nano

and it’ll show you there it is I’m gonna hit ctrl X to exit out of it but

there’s another popular command that people like to use called cat cat

basically will go to a file load it into memory and spill it onto the terminal

to the terminal for you. I mean really what it does is it prints to something called standard

output and then the shell interpreter grabs standard output and it you know renders it to

the terminal but we’ll just say that this prints it to the terminal. So if I say cat and the name

of my program then it prints it to the terminal so you can check any program this way. Do yourself

a favor well do me a favor and do cat at the following path etc os release. The etc

The etc directory off of the root of the file system in Linux is usually where all of the

configuration files get stored.

At least the ones that are system wide.

So like system wide programs, their configurations are usually in the etc folder.

So there’s a special file in many operating systems, definitely Ubuntu, called OS release,

which just describes the operating system to you.

So here, if you’re not sure what operating system you’re using, or if you just want to

and kind of see information on it.

Well, you can say cat, etc.

OS release and see your OS.

So there it is, all this stuff.

Pretty fun.

Okay, so we did my program.

Let’s edit my program real fast.

I’m going to go myprogram.cvp.

And if I want to just say, I don’t know,

maybe I want to make this look a little bit more like a program.

So I can say integer main and we’ll just pretend that we’re not going to do any arguments.

Return zero.

So this probably would compile.

I think this would compile.

If not, then you might have to go into the number of arguments and then…

Don’t worry about this.

This is not a programming video.

A character pointer.

I can never remember if the brackets go before or after the variable name.

a new program i usually compile it both ways and see which one works um okay so oh i did it too

fast okay so i edited and uh if i want to just save my changes i’m going to say control o

notice how it asked me again at the bottom do you want to save it under the same name i just say

enter to say yes if i uh wanted to instead just exit the program i do control x and then

inside a weird area where you can’t really hit keys and you can’t exit very

well you might be inside of Vim some some operating system use Vim as the

default or some some programs so I’m gonna just enter Vim manually whoops

what am I doing is it Vim or V so I’m not a Vim user okay there we go so Vim is

like you know it’s very complicated some people say it’s lightning fast and it’s

By the time you need so many features,

you might as well just mount the remote file system

and use an actual graphical editor.

I’m just not a fan.

Don’t hate me.

You know, we can still be friends.

So if you’re inside of Vim, you hit the insert key

and then you can kind of like type and stuff like that.

So it’s whatever, but what?

Insert?

Okay.

I’m getting lost already inside of Vim.

I’m just going to delete this stuff that I created and so if you want to exit from

Vim hit the escape key first to make sure you’re not inside of insert mode or any

special mode and then say shift holen to enter command mode you’ll know you’re in

command mode because you see this little colon here next to your prompt or next

to a prompt and then I’m gonna say write quit write quit means save the file and

and then quit if you want to quit without saving the file you can just put q but uh vim will

complain if you’ve actually changed something and you’re refusing to save the changes so if you are

absolutely sure you want to discard the changes just say yes i want to quit with an exclamation

point so q exclamation hit enter now you’re out of vim hopefully you’ll never go back for the rest

of your life sorry okay so now we know you know a lot of a lot of stuff that we can do in the

Maybe we should learn how to install programs real fast or search for programs.

And then we’ll do a little bit of some graphical stuff.

Alright, so here’s the command that I wanted to remind myself of.

So how do we search for programs?

If you didn’t know this already, almost every single Linux distribution has a repository

of pre-compiled programs that are open source that you can use for free.

better and a lot safer than the old Windows method of just sort of like going

to random websites online and downloading programs and just kind of crossing your

fingers that you didn’t just download a virus.

What happens is the people who run the operating system, they’ll take the source

code for popular programs and packages.

They’ll compile it for you.

They’ll store the binaries, which are just the compiled executable files.

And then you can use certain command line tools to install those programs one by one.

those programs one by one there’s so many available that it wouldn’t make sense to install them all

by default because you’ll probably never use the vast majority but so we have a nice package

manager in ubuntu called apt it’s the apt package manager if you want to see more information about

it let’s see is it called aptitude or just apt we can say man apt yeah it’s just a command line

interface this actually i think this talks to d package under the hood but you know it’s just a

the package manager one of the sub commands for apt is search so we can say uh launch the apt

program with apt then we could say apt i would like you to search and what would you like app

to search for i don’t know how about a program called mousepad it’s one of my favorite text

editors on linux so what it does is it searches the ubuntu repositories and it tries to find you

know a package or a program that matches and if it does it’ll show you the listing okay so what do i

listing. Okay, so what do I have here? Mousepad is already installed on this system. Yeah,

that makes sense because I think I was just using it. And, you know, some other stuff that

you could find. So you can just kind of search for for anything like do you want a free accounting

program that you don’t have to pay for? It’s not necessarily going to be the best, you know,

but it’s free and it works and it’s good and a lot of people swear by it. Well, you can search

and there it is i don’t have it installed on this machine but new cache free accounting software

do you want to learn to make memes against your enemies well there’s a program for that called

gimp it’s basically it’s kind of like at this point i think an old school photoshop clone

not clone but alternative it’s really good for memes and there are actually a lot of very

talented people who use gimp to do like very artistic things so there it is right there gimp

and it’s GIMP because it’s the GNU image manipulation program.

There’s also another one that’s a little bit more artistic, I think.

I haven’t used it.

I think I used it once.

It’s called Krita.

Oops, sorry, not apt-Krita, apt-search-Krita.

And there it is.

So there’s like a bunch of different choices for any idea that you could have.

Just think of what you want.

You want another browser, another image editor.

You want accounting software.

accounting software you want an audio let’s see is there I think there’s one called our door let

me see apt search you want to like mix music at home so I want to type the name of the program

our door but I want to see if I can find it by just searching for a music term let’s say a

DAW digital audio workstation let me scroll up a little bit yeah there it is okay so I searched

program that came up right here it’s like a very very very popular free and open source

digital audio workstation with like so many tracks that you can mix and and effects and

you can record with it and do all these crazy things um so i’m just trying to show you that

linux is not just for you know coding and and boring stuff there’s there’s a lot of fun stuff

on linux that you can access for free uh through these repositories okay so let’s actually install

Suppose I’m ready to make memes against my enemies.

So I’m going to say sudo apt install instead of search install.

And I’m just going to type the name of the program GIMP.

Oh wait, hang on.

I’m not supposed to show you sudo just yet.

So let’s do sudo, let’s do apt install GIMP.

By the way, sudo is supposedly outdated and people are saying you should use something

else, but I don’t know.

Old habits die hard.

apt install GIMP, the system is telling me that I don’t have permission to install a program

on this machine. And that makes sense. That’s probably a good thing, right? You don’t want to

just let any user totally, you know, redo your system. So it’s saying, you know, could not open

the lock file permission denied. Oh, no. Unable to acquire the d package front end lock. Are you

root? Oh, okay. So what this is basically saying is that in order for us to do root level activities,

like install a program on the system, we need to elevate the command line to root.

And how we do that is we pretty much just say sudo, which is the name of a program that

helps us quickly elevate. It also actually does like a lot of other stuff, but

for now, we’re just going to use it to elevate the command up to root.

So if I say sudo apt install gimp, what’s happening is the sudo program gets invoked,

and then it just executes apt install GIMP as root.

Let me just prove to you that sudo will elevate a command.

So if I go, who am I?

It’ll tell you the name of the current user.

If I say sudo who am I,

then sudo will launch who am I as the root user.

And then who am I should tell us,

whoops, got to enter the sudo password.

You actually have to be an admin to use sudo, just FYI.

So if I say sudo who am I, notice how it prints root.

So if I say sudo apt install gimp, it’s really just going to invoke apt install gimp as the

root user and it should allow me to install that program.

Gimp is already installed.

Okay, I guess I was making memes earlier and I forgot about it.

Well we could remove it.

Gimp.

Then it removes it.

Yes.

I don’t think I was making memes on this machine.

I think something funny is going on here.

And now that it’s removed, I could install it again if I wanted to.

I could say sudo apt install Gimp, and then it might ask you to push yes and enter.

And then it just kind of finishes.

Also if when you’re trying to install things, you get a message that says, repository could

like a 404 error cannot be connected to not found your repos out of date you know whatever that

might just mean you need to update your system so i’m going to say sudo apt update telling apt that

i would like to update its idea of all the packages and then sudo apt upgrade

so update just contacts the server and gets an idea of what packages there are and their versions

the system or it actually upgrades the system when you’re done with that you

usually want to do auto remove to just kind of get rid of any junk that’s left

over if you happen to remove things recently this stuff up here this is sort

of like a corporate upsell you can probably ignore that at least for now

but yeah so we know how to like do lots of stuff in the terminal just just to

open up the let’s see we’re inside of the temp folder okay so I have the temp

folder inside the terminal I’m gonna open up my file system here and I’m gonna

go into the same path so we were inside of let me just show you again with PWD

we were inside of home mic documents temp so let me go inside of the home

folder it’s not downloads documents temp and notice how I have the same file

I can right click on this or even double click on it and I can open it up with

Mousepad or even this nifty little code editor called genie if you’re interested in genie

It’s actually pretty nice pseudo apt install genie and it’ll tell me that this program is already installed

I like to use it because you know vs code and other IDEs. They’re great for productivity

But they kind of help you a lot and if you’re trying to learn, you know coding or whatever

or whatever sometimes it’s a little bit better if you just use something kind of plain because

then you’ll learn more it’s harder uh you know that’s up to you anyway so i’m gonna right click

on this and i’m gonna say let’s open this up with the how about mousepad i guess

now i am graphically editing uh this file because maybe maybe you want to you know edit everything

in nano maybe you don’t maybe you only want to use the terminal when you have to but uh well

have to but well here you are let me do a cat command let’s see my program cat

notice how it’s the same exact file I can I don’t know maybe put some empty

comments up above the function name for fun and save the document and then just

kind of do the cat command again and you can see that my changes have been

updated so you can delete in the regular file system here in XFCE the file

thunar and there should be a symbol somewhere or if you just kind of hit the start menu let’s see

how about office where is thunar usually oh it’s in accessories okay and then if you’re on a gnome

uh it’s probably just called files or i forget what the name of the file system is but you know

something that just looks like a folder um so we’ve edited that we’ve got all the basics here

we know how to navigate we know how to get to our home folder we’re like making directories

deleting directories removing files touching files editing files we’re doing a lot and just to let

you know there’s like so much more you can do on the terminal for instance you can let’s see do we

have gcc on this computer no gcc is what people use to code in c plus plus right so i’m gonna say

package on Ubuntu called build essential.

I think it’s singular, not plural.

And this is sort of like a meta package, which means it’s like a dummy package

that installs a bunch of other packages.

So build essential.

It’ll grab all these other programs for you for like,

it looks like a bunch of C++ stuff and there should be like GNU Mac in there

and some Perl stuff, I guess.

Yeah, I’ve never actually looked at this.

That’s not a lot of stuff that I use.

There’s just a few things that I use in there.

But anyway, you install that and then you’ll get GCC,

which will help you code in C++.

You can also do sudo apt install,

Yasm to install your assembler.

What else?

So GCC and G++ and Yasm and make and an editor.

I think that’s kind of like almost all you need.

Well, you can install a debugger,

Well, you can install a debugger sudo apt install

GDB to install your GNU debugger, which is already installed.

Okay.

Anyway, well, just to let you know, we can do GCC to compile some programs.

It’ll complain.

We don’t have anything.

Let’s see.

Actually, let me go in there.

Let me go to documents temp.

Let’s see if it’ll compile this just as is GCC my program output.

And I’ll just say that we want a program called main.

It’s going to work.

main is this going to work did it actually work oh my gosh i got it right on the first try even

though it was an empty program doesn’t really do anything oh by the way um in linux or in the

command line you probably will see a lot of people do this sort of thing where it’s like dot

slash in the name of a program the thing is in order to execute a program uh i’ll tell you about

permissions in a second first it needs permission to execute but then you need to provide a path

path to the program. You can’t just type main as is because the system, you know, the shell is going

to think that you’re talking about a system program somewhere. So it’s going to look in all the system

areas and it doesn’t find a program named main. So you have to give it a path to your custom

programs to run. So I’m going to say dot slash main. And basically remember the dot was a special

directory that meant the current directory. So if I type dot main, it’s actually kind of the same

home mic documents temp main.

So if I just type this whole path right here, it runs the program

or I can do, you know, dot slash main.

It also runs the program.

In both cases, it works.

Let me edit this real fast to see if I can just get something exciting going on here.

I’ll stream and then I’m just going to go.

Okay, so I’m just going to like do that.

just gonna like do that let me try to compile again gcc my program output to

execute what called me oh what did I do wrong oh gcc is for just regular C

programs you’re not supposed to do that I want to use G plus plus and then I’m

gonna say standard library I don’t know C plus 21 or something std what did I do

Is 21 not a valid year?

I don’t even remember.

I’ve been using C++17 forever.

What did I do wrong?

STD equals C++.

Okay, 17 I know definitely works.

What am I doing wrong here?

Okay, so 17, I guess 19 wasn’t a thing.

Been using 17 for a long time.

Okay, so I just compiled the program again with the C++17.

Well, then what the heck was I doing yesterday?

Was I using 23?

Hang on, sorry.

I forgot what standard I was on yesterday.

Okay.

So then if we run the program again, it prints a message.

So maybe I should retitle this video, your first C++ program, because that’s literally

what we just did.

You know, I’ll make another video.

the basics of the Linux command line.

And well, you’re off.

Well, I hope you enjoyed this video and you learned a little bit of stuff.

Keep watching all the other videos and I’ll see you in the next one.

Hey, everybody.

Thanks for watching this video again from the bottom of my heart.

I really appreciate it.

I do hope you did learn something and have some fun.

If you could do me a please, a small little favor, could you please subscribe and follow this channel or these videos or whatever it is you do on the current social media website that you’re looking at right now.

It would really mean the world to me and it’ll help make more videos and grow this community.

So we’ll be able to do more videos, longer videos, better videos, or just I’ll be able to keep making videos in general.

So please do me a kindness and subscribe.

the middle of the night and I just wake up because I know somebody subscribed or followed.

It just wakes me up and I get filled with joy. That’s exactly what happens every single time.

So you could do it as a nice favor to me or you could troll me if you want to just wake me up in

the middle of the night. Just subscribe and then I’ll just wake up. I promise that’s what will

happen. Also, if you look at the middle of the screen right now, you should see a QR code which

you can scan in order to go to the website, which I think is also named somewhere at the bottom of

to my main website where you can just kind of like see all the videos i published and the services

and tutorials and things that i offer and all that good stuff and uh if you have a suggestion

for uh uh clarifications or errata or just future videos that you want to see please leave a comment

or if you just want to say hey what’s up what’s going on you know just send me a comment whatever

i also wake up for those in the middle of the night i get i wake up in a cold sweat and i’m like

it would really mean the world to me. I would really appreciate it. So again,

thank you so much for watching this video and enjoy the cool music as I fade into the darkness,

which is coming for us all.

Thank you.

The post Ultimate Beginner’s Guide to Linux Command Line: Ubuntu Terminal Basics & More appeared first on NeuralLantern.com.

Hey there! Ready to crack the code on IEEE 754 floating-point numbers? In this video, I break down how to convert decimals to binary and back for 32-bit and 64-bit floats with clear, easy-to-follow steps. From scientific notation to biasing exponents, I’ve got you covered with examples (like 45.84375!). Perfect for computer science students, programmers, or anyone curious about how computers store fractions. Pause, rewind, and learn at your pace! Subscribe for more, check my other videos, and drop a comment with your thoughts!

Introduction to IEEE 754 00:00:00
Prerequisites for Understanding 00:01:03
Steps to Convert Decimal to IEEE 754 00:02:31
Bias and Exponent Explanation 00:03:17
32-bit Float Layout 00:04:09
Sign Bit and Fraction Bits 00:05:44
Example: Decimal to 32-bit Float 00:07:56
Converting 45.84375 to Binary 00:08:34
Scientific Notation for Binary 00:09:05
Biasing the Exponent 00:10:26
Placing Bits in Layout 00:11:17
Final 32-bit Float Representation 00:13:32
Example: IEEE 754 to Decimal 00:14:28
Extracting Sign, Exponent, Fraction 00:15:36
Unbiasing Exponent and Reconstructing 00:16:23
Converting Binary to Decimal 00:18:53
Introduction to 64-bit Floats 00:19:47
64-bit Float Layout and Bias 00:20:05
Example: 64-bit Float to Decimal 00:21:09
Processing 64-bit Float Bits 00:22:05
Reconstructing 64-bit Scientific Notation 00:23:26
Final Decimal Conversion for 64-bit 00:25:00
Conclusion and Recap 00:25:54
Call to Subscribe and Outro 00:26:36

Thanks for watching!

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Hey there! Let’s talk about IEEE 754 floating point numbers stored inside of your machine.

What the heck am I even talking about? Well, uh, there’s a standard called IEEE 754 which governs

how floating point numbers are stored inside of your computer on x8664 machines. So, you know,

of watching this video you probably already know how to convert binary back and forth you know

between binary and decimal and hopefully you understand how to do binary with fractions

if you don’t i have other videos i’ll talk about that in a second and you also understand

that in the machine there is like a slightly different format that’s my doggy slightly

different format for storing signed integers in the machine okay so floating point numbers have

an even different uh format that we have to follow and the hardware is designed that way

hardware is designed that way so before we can really benefit you’re all gonna

see how bad I spell okay before we can benefit from this video your prerequisite

knowledge should be that for starters you should be able to convert back and

forth between binary and decimal including numbers with fractions so if

if you don’t know how to do that yet this video is is not for you just yet you

should go check out my other videos I explain in other videos exactly how to

do that go to the other videos come back and then check this one out after you

know how to convert back and forth between binary and decimal with

fractions the second thing you should know how to do before watching this

video is convert binary numbers with fractions to scientific notation and

and back again. Meaning you should understand scientific notation and you should also understand

how to take a binary number with a fraction and convert it to scientific notation and then

convert it or deconvert it back to like regular form. Again, I have another video for this,

so if you don’t know how to do that yet, you should probably pause this video and then go

Let’s see. For converting from a regular number to IEEE floating point number in the machine using just binary alone is the following.

So I’m going to say basic steps. Step one, convert the decimal number to binary if needed.

And I say if needed because I don’t know, maybe you started with a binary number so you don’t actually need to convert it.

it but I’m just going to assume that you have a decimal number so you’re going to convert it to

binary first then convert the binary number to scientific notation I don’t know if convert is

the right word here because we’re not actually changing the value of the number we’re just

changing the representation so convert it to a scientific notation form maybe would be better

step three we’ll add a bias to the exponents of the scientific notation form what do I mean by

notation form. What do I mean by that? You know, if you have like a binary number and it’s in

scientific notation format, it’s going to look like this. I liked when I’m doing IEEE 754,

I like to keep the right side of the number in decimal. I’m sorry if this confuses you, but

it’s not really necessary to convert this to binary when we’re just trying to convert back

and forth between IEEE. So I always say two to the something power rather than one zero to the

something power because I want to stay in decimal. So I’ll say, you know, two to the seventh power,

right? What this means is that seven is the exponent and I have to bias the exponent before

I put it into the machine. So maybe it’s worth understanding or maybe copy pasting right now

that the bias for 32-bit floating point numbers, I should probably, I’ll paste the whole thing here.

Okay. So here’s like the format for a 32-bit floating point number. We’re good about this

number. We’re good about this just for a second. The bias for 32-bit floating

point number in IEEE 754 is 127. So that means I pretty much have to just take

the number 7 and bias it by adding 127 to it. After I’ve done that I can convert

the biased exponent to unsigned binary whole number. To an unsigned binary whole

number. So step four here is just regular decimal to binary conversion. So I would take, you know,

seven plus 127. The result of that, which I think is like 134, maybe we’ll just be converted into

binary and unsigned binary integer, not two’s compliment or anything like that. Then step five

is respect the layout. So I just, I just copy pasted the layout up above and the layout is this.

you can see that here let me see if I just maybe paste this down at the bottom

you can see that we actually have 32 bits here if I count them for you real

fast we’ve got one for the sign and then we’ve got I can never remember this I

think it’s eight for the exponent one two three four five six seven eight got

eight bits for the exponent that means I’ve already used nine of 32 bits so

that means I should have like 23 bits here so one two three four five six seven

11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, just to double check.

So we know what the sine bit is.

Actually, we don’t yet know in this video.

So in this video, the sine bit, it’s always going to be a zero if the number is positive

and a one if the number is negative.

So that’s the sine bit.

The biased exponent bits go there.

And then these Fs, those are just the fractional bits.

just the, you know, like the mantissa or the mantissa part of the fraction. So imagine if we

have a number like this, all I’m saying is we would copy paste those numbers right here.

Notice how I’m ignoring that first one dot something, because when you put binary in

scientific notation, the first number is always going to be a one. So it can be assumed. There’s

no point in storing it inside the machine. And then if you don’t have enough digits to

you will literally just pad with zeros on the right side because padding with zeros on the right side of a fraction

doesn’t actually change the value. One, two, three, four.

If I put the zeros on the left side of the fraction, it would make the fractional part smaller and smaller.

So that would be bad. I don’t want to change the value.

And this is the opposite of how you pad a whole number.

If I put numbers on the left side of a whole number part, I’m not changing the value.

But if I put numbers on the right side of a whole number part,

which in this case would be the biased exponent, then I would be changing the value.

So we wouldn’t want to do that.

changing the value so we wouldn’t want to do that. Anyway I’m going to remove this and just stick

with step five so let’s see 5a is place the sine bits step 5b is and I’m going to do an example

for you don’t worry place the exponent bits and then 5c is place the fraction bits everything

the first one dot from scientific notation form.

Again, because the first one is implied, it will never be a zero if you’ve done it correctly.

If you end up with a binary number that looks like this in scientific notation, then you’ve

done something wrong because the first number is supposed to be a one.

Okay, so we have those basic steps.

And now let’s do an example.

1, 2, 3 example. Let’s convert decimal to IEEE 754 32-bit float format.

AKA single precision floating point number. Double precision floating point number is 64-bit.

We’ll do an example for that at the very end of this, but I’m just going to stick with 32 and do

number 45.84375, just double checking, and then we’ll convert to binary. Again, this knowledge

is contained in a different video. So if you don’t know how to do this yet, you’ll need to go see my

other video. And so you can see it’s, you know, 45.84375 in binary is just going to be this.

I’ve padded it with two zeros to the left just because, I don’t know, I have a habit of wanting

wanting everything to look like it’s inside of 8-bit chunks.

You can see there’s 8 bits here.

But really, I can just remove those first two numbers.

It doesn’t matter.

Convert the number to binary.

Then, I have to convert the binary number to scientific notation.

I’m going to put maybe pseudo-scientific notation

because I’m not going to convert the right part

where it’s the exponent into binary.

I’m going to keep it in decimal.

Just to clarify again,

convert a binary number to scientific notation and you were actually going to publish it somewhere

or give it to someone, then you should convert the right side. It’s just that I’m not going to

because I don’t really need to convert the right side. I’m not interested in having the whole

number in scientific notation in binary. I’m just interested in what the fractional bits are and

then what the exponent is going to do. Like how many positions to the left or right is it actually

going to move the decimal point? And that’s just going to be the number five, five times to the

five you know five times to the left or to the right so I’m gonna go pseudo

scientific notation you pretty much you know as I covered in the different video

all we’re gonna be doing is just moving the decimal point over one two three

four five until there’s a one in the leading spot and then account for it by

saying times two to the fifth power to say the number is a lot bigger than it

looks so that’s that and let’s see if there are any trailing zeros that’s

Let’s see if there are any trailing zeros, that’s okay on the right side of the fraction.

They don’t actually matter.

You can also just delete them if you want.

Then we need to bias the exponents.

So how do we bias the exponent?

The exponent is just the number five.

That’s see, I was telling you like I don’t really care to convert it to binary because

I’m just going to bias it first and then after that I’ll buy it or I’ll convert it to binary.

So biasing it is just basically adding the bias.

just to make sure that it’s on this page and it’s easy to see.

So I’ll do that.

So in the 32-bit float layout, the bias is 127.

So I’m going to add 127 to 5.

The final number is going to be 132.

So that’s the biased exponent now.

Then I convert the biased exponent to binary.

And that’s going to be this.

10000100.

Then set up the layout so you don’t get confused.

This step is crucial.

Everyone always gets confused by the layout because like we’re human beings.

I can’t count 32 zeros that are all like in the same area and like, you know, and not

get confused every single time.

I mean, I guess I won’t get confused half the time, but that’s not good enough.

So step one is place the layout for yourself so it’s easier for you to place the bits.

place the bits and I wrote this at the top 8 bits and 23 bits just as a reminder double check

yourself 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 that’s 23 bits 1 2 3 4 1 2 3 4 that’s

8 bits we don’t need to remember that the sign bit is one bit for now it’s not too hard so now

let’s place it so the first thing to note is that this number was actually positive positive is

the negative sign there, but if it makes you feel better, we’ll just put a positive sign there just to clarify and be specific.

So because the number is positive, the sign bit is going to be zero. If it were negative, it would be one.

Then we will put the biased exponent bits. So we already converted up there. So I’m just going to copy paste it here.

We’re pretty lucky that the bits are just as big as the number of biased exponent bits that are available.

But suppose for the sake of argument that we had,

the sake of argument that we had just like you know this small number here for the biased exponent

what would you do with the remaining spaces you would just pad with zeros to the left

because remember in whole numbers in binary and decimal you pad to the left you’re not actually

changing the value you definitely would not want to pad to the right but you got to put

a bit in every position it’s got to be something so i’m just going to pad with zeros

then we take the fractional part from the scientifically notated form so that’s just

form so that’s just this right here notice how I’m copy pasting every bit

except for the one that starts the number I’m not going to do the one dot

part because that’s always assumed so we don’t need to store it it wouldn’t make

sense I’ll copy paste the fractional part and I’ll just stick it down there

and now we have a bunch of leftover bits that we need to fill out with the

fractional part you pad to the right not to the left so I’m just going to put

zeros to the right because that won’t change the value of the fractional part

Now we’ve got it. I’m just going to double check my work here.

Oh gosh, it’s too hard to read and then a bunch of zeros. Okay.

Then remove these spaces because now that you’ve done your layout,

you actually want to bear in mind that the machine doesn’t have spaces.

The machine is just, you know, a bunch of ones and zeros everywhere.

So I’m just going to carefully remove the two spaces.

And this is it.

for floating point representation of the number of the decimal number positive 45.84375

seems like a lot but it’s not too bad once you kind of get used to the format

and the bias and you already know the other steps of you know converting decimal to binary and back

again so let’s do another number let’s do it backwards so i’m going to open up a new tab here

example, IEEE 754 32-bit float 2 decimal.

Okay, so suppose we started with the following number.

Start with this number.

Oh my gosh, right?

Remember the layout.

So in the layout we have, use the layout.

Maybe I should copy paste the layout again one more time just to make sure that it’s

easy to see.

it’s easy to see. So I’m going to paste it up at the top and well, no, maybe I want this because

this is like a little bit better. I want that version. Okay. So 32 bits, a bias of 127. So

we’re going to use the layout. I’m just going to copy paste the original number and then add

spaces because I know, well, I guess I can copy paste the layout itself right above that number.

I know I need a space right there that’s the sine bit and then I need a space

after that and notice how the numbers all line up so there’s nothing missing

just to double-check yourself okay so I have the layout I know right away that

the number is going to be positive because the sine bit is zero sign is

positive okay so then I need to pull the biased exponent will be biased

the exponent bits only so I’m just going to copy paste those bits and then I’ll

pull out the fractional part first pull out the fractional part I’m going to

copy paste all those bits and maybe I’ll just say zero point those bits because

that’s what I originally grabbed and I can delete all the zeros on the right

side because again that won’t change the value of the fractional part so I’m

going to delete make sure you’re only deleting zeros though delete that now I

I need to unbias the biased exponents.

First, actually, I should, well, let’s convert the biased exponent to decimal.

A little easier.

I guess you don’t have to do that, but it’s a little easier for me.

Pull the biased exponent.

So this number is going to be 132, which I think is what we had last night.

Let me just double check that.

132.

Yeah.

132, yeah so the biased exponent that we pulled out is 132 then we unbiased the

biased exponent so just subtract the bias again in 32-bit format here the bias

is 127 so I’m going to subtract 127 instead of adding 127 so now I know the

real bias or sorry I know the real exponent is 5 then I can recreate the

I’ll put sudo here just because it’s not, you know, I’m not, I’m not converting binary for,

for the entire thing. So that means I can take the fractional part here and I can say it’s going to be

one dot the fractional part. Maybe I should remove that zero here to make it less.

I don’t know. Cause if I put a one there, it kind of feels like I’m saying the number is

that it’s one dot something.

I don’t like that I’m putting a zero there.

I’m just gonna erase it

because it’s really gonna end up being a one.

And if I say pull the fractional part

and I put a one there,

then it doesn’t it kind of sound like

I’m pulling the one from somewhere?

No, the one is implied.

Anyway, so now I can recreate the number

in pseudo scientific notation.

I can say times two to the something power.

We know that the exponent is five.

Again, it’s pseudo scientific notation

because if five we’re gonna do the complete,

complete, you know, true scientific notation. The right side should also be in binary, but I’m not

going to do it. I’m a little bit lazy because we don’t need that IEEE. So it’s going to be two to

the fifth power. Then if I undo the scientific notation, I’m really just going to take this

scientifically notated version and I’m going to say, well, I’m going to move the decimal point to

the right five times because that’s what the part on the right says. So I’m going to go one, two,

1, 2, 3, 4, 5, stick it there, remove the original decimal point, and then I can remove

the exponent part. So then let me just double check my work. 1, 0, 1, 1, 0, 1, 1, 1, 0, 1. Okay.

So we’ve got that now. Then all we have to do is convert this number from binary to decimal.

The final number here is just, you know, it’s going to be the same number that we worked with

number that we worked with previously so I’m just going to copy paste it there is

you know of course this video is not about converting back and forth from

binary to decimal with fractions check out my other video if you want to learn

how to do that but once we do that you know this number becomes that number

and and now we know how to convert back and forth between a decimal number and

for 32-bit floats in the machine.

No problem.

A lot of steps, but no problem once you understand them.

Okay, now let’s do an example

with 64-bit floating point numbers.

Honestly, this is not gonna be more difficult.

In 64-bit floats, the idea and the format and the steps,

it’s all gonna be the exact same thing.

It’s just that we have more bits

for the biased exponent and the fraction,

and then the bias itself will be a little bit higher.

So let me copy paste the format for you to see.

at for you to see. So in IEEE 64-bit floats, IEEE 64-bit float, well IEEE 754, 64-bit float,

you know we refer to these floats as doubles right double precision floating point numbers.

Notice how instead of 8 bits for the biased exponent we have 11 so we can represent a much

notice how for the uh the fraction part instead of having 23 bits we have 52 bits so we can also

represent much more precisely that’s really the only difference let’s uh oh sorry the other

difference is also that the bias is now equal to 1023 instead of 127 so what is that like

10 times larger of a number that we can represent or something like that so mostly we get more

If you don’t like it, sorry, it’s the way it is.

It’s in the hardware.

So let’s do an example for a 64-bit float for a double.

64-bit example.

Let’s say we started with the following number.

Inside of the machine.

Like we looked inside of the machine and we grabbed these bits.

And I’ll get rid of the spaces.

So we have like a giant, big, huge number.

We have like a giant big huge number.

We’re trying to figure out, you know, what is this number in decimal.

So I’m going to add spaces to respect the layout.

I’m going to just copy paste the layout right here.

I’m going to say respect the layout.

I’m going to paste it and then that helps me line everything up.

So I’m going to say the sine bit is the first bit and then I’ll put a space there so I know.

All right, the sine bit is a one.

That means it’s going to be a negative number.

The biased exponent bits are there.

The fractional bits are there.

bits are there so well first thing I can just do is say that the sine is going to be negative

because the sine bit is a one

and then I’ll pull the biased exponent bits which is going to be this number right here

should pull the fraction bits next. Fraction bits are just here I’m gonna

copy paste those here and then I can remove the zeros. Be very careful you’re

not removing any ones. So there was a lot of wasted bits there. That’s okay. I’ll

convert the biased exponent to decimal. So that’s going to be…

I think and I did not do that in my head.

I have an answer sheet.

Don’t worry.

I’m not that cool.

Then we’ll unbiased or de-bias unbiased the biased exponents by just subtracting the bias.

Remember in this 64 bit format, the bias is 1023.

So that means I got to take 1031 minus 1023 and that will be equal to 8.

Okay.

Okay, now we kind of have everything we need to sort of reconstruct the scientific notation part, right?

We have the fraction bits, that’s the most important part.

Oh, and then also the sine bits.

So I can say negative something.

It’s obviously going to be one dot something because even though the number is negative,

it will still always start with a one.

That rule doesn’t change.

Negative one dot something and I’ll just paste the, whoops, paste the fraction bits.

I think I did paste the right thing.

right thing so we paste the fraction bits and then we have to use the regular exponent the

unbiased exponent the non-biased exponent two times times two to the oops times two to the eighth power

now this is our number in scientific notation um

convert to scientific notation i’ll put p for pseudo scientific notation

and then now we have to convert to just regular format okay so I’m going to

copy paste this right here and if it’s 2 to the eighth power that means the real

number is going to be bigger than it looks in scientific notation even though

if you are very familiar with scientific notation you kind of already know that

it looks big but you know if we just if we’re only talking about the bits on the

1, 2, 3, 4, 5, 6, 7, 8.

Put the decimal point there.

Remove the original decimal point.

Now we no longer need 2 to the 8th power.

And again, just as a reminder, if it was 2 to the negative 8th power,

you would be moving the decimal point in the other direction.

So now we’ve got this number 111, 010101, 0101, 0101, 0101.

Then a 0.01.

Okay, so then convert to decimal.

doesn’t talk about how to convert back and forth from binary to decimal find my other videos but

basically uh it’s going to end up being six uh negative four six nine point two five

okay we now have done a quick practice starting with a giant number of bits and slowly converting

them to the real uh floating point number in decimal that uh that they represent i’m not going

going to do another number in the reverse direction because we already did that for 32 bits

and again with 64 bits the only real difference is just you have more exponent and fraction bits

and the bias is a higher number and that’s it so like all the other steps are just the same

I just wanted to show you one time with a 64-bit number in one direction but

I think at this point we’re good thank you so much for watching this video I hope you learned

had a little bit of fun. I’ll see you in the next video.

and grow this community so we’ll be able to do more videos, longer videos, better videos,

or just I’ll be able to keep making videos in general. So please do me a kindness and subscribe.

You know, sometimes I’m sleeping in the middle of the night and I just wake up because I know

somebody subscribed or followed. It just wakes me up and I get filled with joy. That’s exactly what

happens every single time. So you could do it as a nice favor to me or you could troll me if you

want to just wake me up in the middle of the night, just subscribe and then I’ll just wake up.

just wake up I promise that’s what will happen also if you look at the middle of

the screen right now you should see a QR code which you can scan in order to go

to the website which I think is also named somewhere at the bottom of this

video and it’ll take you to my main website where you can just kind of like

see all the videos I published and the services and tutorials and things that I

offer and all that good stuff and if you have a suggestion for clarifications or

or errata or just future videos that you want to see please leave a comment or if you just want to

say hey what’s up what’s going on you know just send me a comment whatever I also wake up for

those in the middle of the night I get I wake up in a cold sweat and I’m like it would really it

really mean the world to me I would really appreciate it so again thank you so much for

watching this video and um enjoy the cool music as as I fade into the darkness which is coming for us

Thank you.

The post Master IEEE 754 Floats: Binary to Decimal Guide appeared first on NeuralLantern.com.

Ready to conquer binary scientific notation? Let’s make it fun and simple! In this video, I walk you through how to represent binary numbers with fractions in scientific notation—a must-know skill for computer science, programming, and understanding IEEE 754 floating-point representation. We start with the basics of scientific notation in decimal (think 8.54 × 10⁵), then dive into binary with clear, step-by-step examples. You’ll learn how to handle large and small binary numbers, move decimal points, and use base-2 like a champ. Whether you’re a student, coder, or just curious about how computers process numbers, this video has you covered!

I’ll show you practical examples, like converting huge binary numbers and tiny fractions, plus tips to avoid common mistakes (like mixing decimal and binary notation). By the end, you’ll be ready to tackle binary in IEEE 754 or impress your friends with your number-crunching skills. Subscribe for more tech tutorials, and hit that bell to stay updated! Visit my website (link below) for more resources, and leave a comment with your questions or video suggestions—I read every one! Let’s keep learning and having fun with tech together!

Introduction to Binary Scientific Notation 00:00:00
Purpose of Binary Representation 00:00:12
Overview of Scientific Notation 00:00:41
Rules for Scientific Notation 00:01:12
Decimal Scientific Notation Example 00:02:26
Practice with Large Decimal Number 00:04:12
Practice with Small Decimal Number 00:05:21
Binary Scientific Notation Concept 00:06:32
Binary Number Representation Rules 00:07:28
Large Binary Number Example 00:08:24
Small Binary Number Example 00:09:31
Mixing Binary and Decimal Notation 00:12:54
Pure Binary Scientific Notation 00:13:04
Connection to IEEE 754 00:13:48
Conclusion and Call to Action 00:14:21
Engagement and Website Promotion 00:15:32

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Hey there! Let’s talk about representing binary numbers with fractions in scientific notation.

Why would you need to do this? Probably the best use that I can think of off the top of my head

is being able to represent binary numbers with fractions inside your machine in a format known

It’s just a crucial step before you can represent numbers inside your machine using IEEE 754.

Okay, so first off, let me just show you a little bit here about scientific notation.

So you probably have seen something like this before where it’s like 8.3873,

and then you’ll see like a multiplier times 10 to the fifth power, right?

I can’t really type this out very well, so maybe I could just draw it for a second, you know.

well so maybe I could just draw it for a second you know 8.54 times 10 to the fifth power right

that’s what I’m trying to convey but anyway so about scientific notation itself it’s standardized

so that it’s easier to use and that is you know it’s just like faster for everyone to understand

and there’s less confusion part of the standard is that you always want to have a number on the

that is between 1 and 9 inclusive. You don’t ever actually want to have a 0 there that would be bad.

You don’t want to have a 10 or anything greater that would also be bad. You just want to have

1, 2, 3, 4, 5, 6, 7, 8, 9 on the left side. And then on the fractional side,

you want to have a number that just kind of like helps you represent the entire

original number without losing precision. And then on the right side, you want a number,

a number, let’s say like x to the y power, where x is the base of the number system you’re working

in. So this is decimal. The base for decimal is 10. So we’re going to say 10 to the something

power. What is the power? The power here helps you understand how big or small the number on

the left really is. That’s kind of one of the benefits of scientific notation. It seems to

help you understand a little bit more of how big or how small a number is rather than exactly

than exactly down to you know the last digit what what is the number precisely so we could say for

now it focuses more on largeness or smallness than preciseness what number are we actually

representing with this in scientific notation well times 10 to the fifth power just means move the

decimal point over a certain number of times so uh you know that’s why we have 10 to the something

go left or right in a base 10 number you’re looking at a different number that has a factor

of 10 for its strength in either direction like multiply by 10 multiply by 10 multiply by 10

or divide by 10 divide by 10 divide by 10 in the other direction so this means we want to move the

decimal point five times to the right to increase the strength of the number times five so one two

three four five if we put the decimal number there then this is the number we were going to represent

number we were going to represent originally so if somebody says hey give me this number 838730

and put it in scientific notation then you your first instinct is to say all right let’s uh type

that number out and we’ll put like a dot zero there and it will just we’ll move the decimal

point over until there’s only one digit um and it’s a you know somewhere between a one and a nine

three four five times over in order to get the decimal point there so that

means it’s going to be this times 10 to the fifth power because we moved it over

five times and you can see that’s the original number that I showed you these

zeros at the very end they don’t actually mean anything so we can omit

them probably a smarter idea to omit them and that’s why we see numbers that

way okay so keep that in mind there’s only one digit let’s maybe do like

practice number here I have a couple practice numbers written down already

let’s see so we’ll start with this number a huge gigantic number just to

practice if we copy paste this down to the next line and then we decide all

right how many times do we need to move the decimal point to get the decimal

point right there so that the two is the first number remember one to nine

inclusive so I’ll just I’ll use two decimal points so I can count more

9, 10, 11, 12, 13.

So that means I did 13 moves.

I’ll put 13 right here so I don’t forget.

Times 10 to the 13th power.

And the 13 is positive because when we’re looking at the scientifically notated format

of the same number, you know, 2 point something is way smaller than the original number.

So we want the scientifically notated format or form to get bigger in order to reach this

number.

in order to reach this number so that means 10 times sorry times 10 to a positive number positive

means it’ll be bigger in its original form okay so now let’s do another practice number

let’s do a number that’s really really really small like you’re inside of inner space or

something so we start up with this number and we still want to have a number between

rewrite it here I really want to have eight point something because that’s the first number that’s

bigger than zero that I can see so again I’m using two decimal points so that it’s easy for me to

count I’m going to go one two three four five six seven I had to move it seven times so it’s going

to be negative seven is going to be the exponent so you know raised something raised to the negative

seven it’s still going to be 10 to the negative seven that I multiply it by so then I’ll say get

And now this is the same number represented in scientific notation.

It should have all the same digits.

The decimal point basically should just be moved.

Of course, you know, when you represent in scientific notation,

depending on what standard you’re working with,

you might actually omit some of the numbers at the very end of the fraction here.

But that’s why we say this is kind of more to impress upon you the smallness or largeness of a number

rather than represent the number exactly precisely.

okay so we got that two practices in there how can we do this same exact concept in binary

well keep in mind in binary binary is a base two number this video is not about binary conversion

as a whole number or binary with fraction let’s just pretend that we already know how to do that

and we have a binary number to start off with so let me grab my example number here

have some kind of a binary number with a fraction, which you can do if you don’t understand how to do

this part yet from decimal with a fraction to binary with a fraction or back and forth.

See my other videos. For now, we’ll assume you can do this. So how can we get this in scientific

notation? So the first thing we have to understand is that it’s going to be, you know, some number

right because that was the format we used before the number should only start with a one it should

never even start with a zero remember in binary we can only use ones and zeros before i said here

let me just show you this real fast again before i said the starting number has to be one through

nine inclusive that was because in decimal we have zero one two three four five six seven eight nine

be only use you know one two three five six seven eight nine so but in binary um i’ll put like

a character set like the available characters we can use to represent the numbers in decimal

so in binary the care set that we can use is just you know a zero and a one only but the same rule

the one so that means the first number always has to be one it has to be always one dot something

for our purposes to represent the same number in scientific notation so it’s going to be

this and obviously that one has to be it it cannot ever be a zero so i’m going to put the

decimal point there uh and then i’m just going to count like how much did i actually move the

seven eight nine ten eleven twelve thirteen fourteen fifteen six just fifteen just fifteen not

sixteen so i’m going to put times something to the fifteen power and remove that other decimal

point and then the base is two so it’s going to be two to the fifteenth power

so now maybe i should move that up a little bit

gigantic number uh in scientific notation it’s going to look a little smaller but then the times

base to the 15th power is going to help us understand how big it is oh it’s like pretty big

let’s do the same thing backwards let’s say that we wanted to start off with a very very small

number so it’s like you know a zero point something in binary so you can imagine if this is like one

256 that’s probably going to be a number that’s no bigger than or just like slightly bigger than

256 so it’s going to be like kind of a small number right well we’ll do the same thing just

copy to another line and then make sure that the decimal point sits in a place where there’s always

a one at the start

and then just count the number of times you moved

number of times you moved the number oh I guess before we would have possibly

deleted numbers on the right if we were gonna reduce precision in this case

after we count the numbers we’re gonna remove everything to the left of the one

so that the one is in the first position and I’ll just go ahead and do it okay so

how many times do we move it one two three four five six seven eight that’s

eight times so I’m gonna put an eight there just to remind myself that there

will be an eight I’ll remove all the stuff at the beginning that doesn’t

all the stuff at the beginning that doesn’t matter anymore and it’s going to be times two because

that’s our base to the eighth power but the original number is a lot smaller than the

scientifically notated number looks so that means we have to put a negative eight because remember

when you say times let me just show you this on a calculator when we say let’s let’s go back to

fifth power then you know that we’re just basically adding four zeros right so

like we have five total zeros so we’re adding four zeros to the ten but if we

did to the negative five power we’re gonna be like dividing it by ten a bunch

of times so instead of multiplying it by ten for a total of five times we’re

gonna divide by ten so then the number gets really really really small so that

means when we say two to the negative eight power we’re gonna be dividing it

We’re going to be dividing it by two that many times.

And so we end up with a really, really, really small number.

Isn’t that what I kind of said?

Let’s see.

I mean, like, not exactly, but, you know, it’s like 0.003 and then some numbers after that.

Didn’t I say one divided by 256?

It’s 0.003 and then some numbers.

So this number is just a little bit bigger than 0.003.

Nine.

Let’s see how much bigger it is.

bigger it is point three six two five what

oh because i’m not i’m not including the the part on the left that we will multiply it by so if i

you know if i did some like binary up here and i was in binary mode then it would probably make

more sense it ended up being exactly the same exact number that’s why i was confused because

if we just type that part on the right side then it really is going to be one over 256.

Anyway, long story short, we have this number here, the fractional part, and then we’re

going to multiply it by two to the something power.

Notice something in particular that I’m doing, which is probably my mistake, but I kind of

like doing it this way.

Notice how the left part is in binary and the right part is in decimal.

There’s no number two in binary or no number eight in binary.

numbers like this to scientific notation so that you can convert a binary number to i triple e

floating point number this is as far as you really need to go but if you truly want to represent a

binary number in scientific notation then you should also convert all of the relevant parts

so how do we represent uh the number two in binary it’s going to be one zero how do we represent the

number eight in binary it’s going to be one two four eight it’s going to be that so uh you know

big number times 10 in binary is still the number two to the something power the negative 1000 in

binary power is going to be you know eight the negative eight power so this is great if you just

want to write an entire number in scientific notation but uh you know in probably my next

video when we talk about ieee 754 notation this is as far as you really need to go

eight number into a a whole number in binary and then putting that somewhere but so just

forget about this for now keep in mind this is how far you have to go if you want to go to ieee

if you only want to be in pure binary then this is what it would look like

okay that’s it uh i think that’s all the example i have for you today in this video thank you so

much for watching i hope you learned a little bit and had a little bit of fun see you in the next

video

Hey everybody!

Thanks for watching this video again from the bottom of my heart.

I really appreciate it.

I do hope you did learn something and have some fun.

If you could do me a please, a small little favor, could you please subscribe and follow

this channel or these videos or whatever it is you do on the current social media website

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do do me a kindness and and subscribe you know sometimes I’m sleeping in the

middle of the night and I just wake up because I know somebody subscribed or

followed it just wakes me up and I get filled with joy that’s exactly what

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And if you have a suggestion for clarifications or errata or just future videos that you want to see, please leave a comment.

or if you just want to say hey what’s up what’s going on you know just send me a comment whatever

i also wake up for those in the middle of the night i get i wake up in a cold sweat and i’m like

it would really it really mean the world to me i would really appreciate it so again thank you

so much for watching this video and um enjoy the cool music as as i fade into the darkness

Thank you.

The post How to Master Binary Scientific Notation (with Fun Examples!) appeared first on NeuralLantern.com.

Struggling with converting decimal fractions to binary? In this fun, beginner-friendly tutorial, we dive into how to convert numbers like 45.8046875 to binary and back to decimal, step by step! Learn the multiplying-by-2 method, handle precision loss, and understand fractional binary representation. With real examples (0.126753, 0.84375), you’ll master this key computer science skill. Perfect for students, coders, or anyone curious about how computers store numbers. Subscribe for more tech tutorials, and let me know what you want to learn next! Visit [YourWebsiteLink] for more. #Binary #DecimalToBinary #ComputerScience #TechTutorials

Introduction to Decimal-Binary Conversion 00:00:00
Understanding Fractional Binary Numbers 00:00:15
Fractional Binary Representation Basics 00:01:00
Converting Decimal Fractions to Binary 00:04:06
Example: Converting 0.126753 to Binary 00:04:52
Precision Loss in Conversions 00:05:36
Example: Converting 0.84375 to Binary 00:09:57
Converting Binary Fractions to Decimal 00:14:22
Example: Converting Complex Number 45.8046875 00:16:48
Combining Whole and Fractional Parts 00:21:00
Conclusion and Verification 00:23:25
Outro and Community Engagement 00:24:16

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Hello there, let’s talk about how to convert decimal numbers with fractions into binary

numbers with fractions and vice versa.

So up to this point, if you’ve been watching my other videos, you probably know that you

can easily convert a decimal number to binary and binary to decimal if the decimal and binary

numbers but in order to progress towards IEEE 754 representation in other words

in order to eventually be able to represent binary numbers with fractions

like floats or doubles in the machine you have to start learning how to get

the fraction part of a decimal number into binary the way we’re going to do

it in this video it’s not actually going to be the final representation of how

your machine stores floating point numbers but it’s an important step on

on the way there. Without this step, you probably wouldn’t be able to do it.

So what am I talking about? I’m just going to open up this notepad real fast and just show you

that what I really mean is, suppose we have like a number 45 point blah, blah, blah, blah, blah,

right? So this is the whole part and this is the fractional part. Okay, no problem. Also in binary,

we have like a bunch of ones and zeros. This is a whole number, but we could put a decimal point

and then just start doing more numbers after the decimal point in order to represent a

in order to represent a fractional binary number.

Okay, so let’s see.

We know, hopefully at this point, if you watch my other videos,

that, I don’t know, I’m just going to put some random numbers here

and then like some more random numbers there.

And you know that the strength of each of these numbers

is sort of like increasing by powers of two on the left side, on the whole side.

So the strength of that first digit is one.

digit is one the next digit has a strength of two and then four and then eight and then 16 maybe i’ll

put the six up here and then 32 so three and two and then 64 and maybe i’ll do another digit i’ll

just put like a zero there and then you know the left most digit has a strength of 128 so basically

a 1 or a 0 for the actual binary number multiplied by its strength. So 1 times 1 is 1, add that to

0 times 2, add that to 1 times 4, and 0 times 8, and 1 times 16, and so forth, right? So hopefully

we know how to do that at this point. To do the same thing on the fractional side, maybe I won’t

put a decimal marker there, it’s really the same deal except as we go left, we were multiplying by

have more power more strength but as we go to the right past the decimal point they should have less

strength and we’ll just divide them by two so pretty much at this point let’s see we’ll have

one half will be the strength of this digit right here whoops one half so the strength that that

digit has is just one half the strength that the next digit has is going to be one fourth remember

1 4th remember you multiply sorry you divide by 2 each time whoops I’m getting lost oh man I

probably need to add some spaces because it’s starting to get pretty ugly so this digit has

a strength of 1 half this digit has a strength of 1 4th and then we’ll just say that the next one

has a strength of 1 8th and so forth we’ll just keep dividing by 2 each time so don’t forget that

don’t make the mistake of saying 1 4th or sorry don’t make the mistake of saying 1 half 1 3rd

one half, one third, one fourth.

Don’t increase the denominator by one.

You want to multiply, or sorry,

you want to divide by two each time.

Or if you want to say the word multiplication,

then you multiply by 0.5, I guess, if you want to.

I’m just going to write 1 16th

and then just be done with the divisions.

I hope you understand what I’m talking about.

We’re going to do some examples right now.

Okay, so let’s calculate.

Well, actually, let’s just, just to emphasize, just to make sure everybody understands, what

we would do to convert such a number from binary to decimal would basically be, you

know, compute the left side as if it were a whole number.

I’m going to put W for whole number.

And then separately convert the fractional part as if it were just, you know, zero point

something.

And then just combine the two things when you’re in decimal.

And you’ll do the same thing when converting a number from decimal to binary.

decimal to binary you convert the whole part first put that into ones and zeros then convert the fact

the fractional part into a fractional binary part and then just combine them across the decimal point

so let’s do an example let’s start with converting 0.126753 i don’t think that this number is going

to resolve easily it’s kind of like a good lesson here when you’re converting between binary and

there are always going to be some numbers in in in decimal that you can’t represent in binary

and vice versa there are always going to be some numbers in binary that you can’t represent in

decimal so it’s not that decimal or binary or you know superior or inferior i mean all technology

is pretty much running on binary so it can’t be that bad but um just keep that in mind some numbers

that you type randomly are just never going to resolve and you’ll have to give up at some point

have to give up at some point and say, well, we’re just going to call this a precision loss

because we just, we just have to like give up, especially if you only have so many bits

to put the fraction in. Okay. So what am I going to do? What’s the, what’s the basic algorithm

here? There are lots of different ways to do it. The way that I’m going to show you is just

multiplying by two. So if we take, you know, 0.126753 and we multiply it by two,

We end up with, let’s see, times 2.

Whoops, hello.

Oh, I got to do that.

Times 2.

We’re going to end up with a different number.

If the number is equal to or greater than 1,

then we will say that we have achieved a number of 1 for the converted binary number.

And if not, we’ll say we have achieved a number of 0.

If the number is 1, we’ll also subtract 1 from the remaining number here in decimal.

The result we have is just, what’s going on?

Oh, I somehow turned on my annotator.

Okay.

In this case, we just have, you know, this number right here.

It’s not greater than one or equal to one.

So I’m just going to say this gave us a binary number of zero.

And because it gave us a zero, we’re not actually going to change it at all.

We’re not going to subtract one from it.

We’re just going to leave it as is.

We will then multiply by two again.

by 2 again. So I’m just going to say, do it one more time. We’ll say this multiplied by 2,

and it’s going to be this number. Again, it did not exceed or equal 1, so the bit in that position

is going to be a 0, and we’ll just copy and carry it over just as is. Do it again, and we’ll say

Now we have a number that equals or exceeds one.

So we’ve achieved a one in the binary position.

So it’s going to be a one here.

Then we got to subtract one.

So we’re just going to be left with 0.014, 024 and whatever.

And then we just continue.

Maybe I’ll do it a couple more times,

but I’m going to give up because I don’t think

that this number will translate completely.

So I’m going to say multiply by two again,

and it’s going to give us,

hang on a second here.

What was that?

Hang on a second here. What was that? That was one. Oh, I forgot to subtract one. So I got to

subtract one. And then I’m going to multiply by two. Now we get this number right there.

This is not equal to or greater than one. So the bit is going to be zero.

And then that means the remaining number is just going to be the same thing.

We’ll do another. Actually, let me let me clean the calculator for a second here.

going to select this whole thing and just paste that and I’m going to say

multiplied by two that’s going to be that new number and I think you’re

starting to understand why I want to give up because we’ll just be kind of

doing this forever this might end up being an irrational number in binary I

don’t really know I haven’t gone that far but it’s definitely gonna take a long

time so I’m gonna give up and I’m just gonna say all right the final binary

number is gonna be 0.00100 and then just say maybe there’s some more stuff at

maybe there’s some more stuff at the end we’ll just call this a precision loss

you can see well maybe I should do one more number actually because it it’s kind of a mirror there’s

like two zeros and then a one and then two zeros on the other side let me multiply this by two

real fast just to show you without symmetry what would happen so I’m gonna multiply that by two

and it’s gonna be this number right here so that’s gonna be zero because it didn’t exceed

or meet one and so the number we have left over is just that okay so now

because there’s no symmetry you can see that the number is going to be point

zero zero one zero zero zero we go from top to bottom we don’t do any kind of

reversal like you might do with whole number binary conversion I don’t know

maybe it’ll be zero for a long long long long time and never or yeah they’ll

probably be some ones in there at least I don’t know if it’s ever going to

resolve you’ll know you’re finished when the

Here is a zero.

So again, I’m just going to give up on this because I don’t really know if it’s going to work.

Let’s do a number that I know is going to resolve.

I have this one prepared in advance.

So let’s do 0.84375.

Okay.

So how do we convert this?

Again, just multiply by two.

Every single time you meet or exceed one, then you’ll say that we have a one in the binary number.

binary number and then subtract one after that and if not we will say that

we have a zero in the binary position and then we won’t subtract one okay so

that number multiplied by two is going to be point one six eight seven five so

that’s definitely greater than or equal to one so I’m going to say we have a one

in the binary position and then the next number is going to be just be zero point

now we take that number 6875 you could also just you know in your calculator you could say minus

one and then we’ll multiply it by two to get the next bit the number is going to be 1.375 so i’m

going to write 1.375 here and then it’s greater than or equal to one so it’s going to be another

one here and then after we subtract one it’s going to be 375 no problem okay so let me just

And then multiply by 2 to get to the next bit position.

It’s going to be 0.75.

All right, so 0.75, that number is less than 1, so we have a 0 in that bit position.

We also don’t subtract anything because we had a 0 in that bit position.

Then we just multiply by 2 again.

Multiply by 2, now we have 1.5 because that’s greater than or equal to 1.

We have a 1 in that bit’s position, then we subtract 1.

one it’s just going to be 0.5 that should be pretty easy right because that’s that sounds

like there’s a one in a bit and then it’s just done after that so i’m going to do minus one

and then multiply by two again notice how that is exactly a one so it’s going to be 1.0

which means we have a one in the position because it is equal to or greater than one

and then uh well what we have left over is zero

Zero multiplied by two is going to be zero.

So that means if we kept doing this forever,

then all the numbers down here are just going to be zeros forever.

And I said in another video,

when you realize what’s going on with the zeros,

like where are they?

Are they on the left or the right?

When you’re converting a whole number from binary to decimal or decimal to binary,

the zeros would be on the left side.

So that’s why we would reverse

because if you just add infinity zeros on the left of a whole number,

you’re not changing the value.

number you’re not changing the value but if you added them to the right you’d be increasing the

value when it comes to the fractions the right side of the fraction won’t change the number for

example if we had you know one point and then some like random binary numbers if we just kept adding

zeros on the right side that’s not changing the value of the number because this is the fractional

part however if we started adding numbers on the left side then we would make the fractional part

smaller and smaller and smaller so that means the zeros have to be on the right side and you can see

and you can see here the right side is the bottom so that means we’re going to take these numbers

I’ll just put etc here just so you can see etc that means we’re going from top to bottom so the

final number is 0.11011 and then a bunch of zeros after that are just you know nothing

and that’s the final answer we now have 0.84375 is equal to binary that number and we’ll just say

that number and we’ll just say OB to to indicate that the following is a binary

number because again you could have a decimal number and then have like a

bunch of like ones and zeros in the fraction part I guess so to make sure

that the reader understands what they’re seeing you’ll say OB to indicate this is

a binary number on exams or quizzes if you’re out there doing this for an exam

or a quiz keep in mind you probably want to talk to professor to make sure that

ob is supposed to be part of your answer they might just want this it depends anyway so 0.11011

okay then let’s convert it back again let’s let’s convert this number to the original decimal number

there okay so how can we do that pretty much just start adding the fractions up so remember the

Remember, the first fraction that we see is going to be one half.

One half.

And the second fraction we see is going to be one fourth.

And then we just keep multiplying.

One fourth, one half.

Maybe I should write this in a notepad here.

We’ll see one half plus one fourth plus one eighth.

And some of these bits aren’t going to count.

Like, for instance, the one eighth, it’s not going to count towards the fraction.

But for me personally, if I forget to type one eighth,

I’m probably going to accidentally use it for the next position.

So I’m just going to type everything one at a time.

So let’s see, we have one, two, three, four, five, one, two, three, four.

So I got to do one more plus one 32nd and then multiply by the bits.

So say like, you know, one times that and then one times that and then zero times that

to basically, you know, cancel it out.

And then one times that and then one times that.

plug it all into the calculator

let’s see if I got that right

0.84375

so that’s how you convert

back from binary to decimal

pretty easy and then also

of course when you’re practicing this you want to try

with a bunch of different random numbers to start off with

you just want to be

careful again this process

could take forever if you have like

you know the wrong number that you

start with but I guess at least

at least when we’re converting from binary to decimal it’s going to end up resolving to something

uh it won’t necessarily be something that you can’t represent but you know if you start

up with a random number in decimal there’s a chance maybe it’s not going to work with binary

okay well you have to give up and call it a precision loss okay so then now let’s uh let’s

ask what if we had a complex number because we know how to do this now with just the fractional

now with just the fractional part but what if we had a number that was um a little bit more

difficult let’s say we have wait a minute you know for you know for 37 5.

oh i think i just accidentally did a totally different number than i wanted to on my plan

luckily i got the right answer okay

Anyway, what if we had a more complicated number?

Let’s see, 804, 6875.

Okay, so 804, 6875, but with a 45 in front of that.

Remember we said before that this is the whole part

and this is the fractional part,

and you just wanna do them separately

and then combine them afterwards.

So the whole part, let’s see, what is that gonna be?

I’m just gonna say that this is not a video

for whole number binary conversion.

This is just dealing with fractions.

just dealing with fractions. Find my other videos if you want to know how to convert the whole part,

but I’m going to say that 45 is just this number in binary. And you can double check real fast.

You can say 1 plus, here let’s do it again, let’s do it just to be sure. 1 plus not a 2 because

there’s a 0 there, and then we’ll say 4 plus 8 plus not a 16 because there’s a 0 there, and then

plus 32. Add that together, that’s 45. So the whole number part is pretty easy if you already know how

number part is pretty easy if you already know how binary conversion but now let’s convert point uh

zero eight zero point eight zero four whoops screenshot no thank you zero point eight oh four

six eight seven five so i’m gonna have to do this from scratch since this is a different number than

i just worked with we’ll do that multiplied by two and it’s going to be this number

is that really not the same number?

Yeah, I guess I really just did a different number.

Okay, so that means we’re going to have a 1 in the binary position

and the remaining fractional part is just going to be this.

Whoops, zero point that.

So then we take that number and bring it down.

Multiply it by 2.

Whoops, not supposed to actually bring that part down.

We’ll bring it into the calculator.

We’ll multiply it by 2.

actually let me get that again and subtract one just to double check myself it’s always good to

double check yourself then we’ll multiply this by two and then the number is going to be point

1.28 so we have that and then since it’s either equal to or greater than one it’s going to be

you know a one in the binary position so 0.21875 is going to be the remainder there

so I’m going to do minus 1 and then times 2 to make sure the calculator agrees with me whoops

21875 okay then I’ll do a multiply by 2 to get the next number 4 3 7 5

and that’s not equal to or greater than 1 so we’ll put a 0 there and we won’t subtract anything

so it’s just going to be 0.4375 again then we’ll multiply that by 2 to get the next number

times two it’s going to be 0.875 so 0.875 again this is not one or greater so we have zero in

the binary position and we don’t subtract anything 0.875 multiply by two again times two so it’s

going to be 1.75 1.75 and then of course we’ll have a one in the binary position and the leftover

0.75 so let me just go back to the calculator and I’ll say minus 1 times 2 it’ll give us 1.5

so 1.5 over here means we’ll have a 1 in the binary position because it was equal to or greater

than 1 the leftover is going to be 0.5 now you know we’re about to finish because 0.5 times 2

is just going to be 1.0 which will give us a 1 for the binary part and then the remainder is going

remainder is going to be 0.0 and then you know there’s no need to multiply 0 by 2 because it is

forever going to just be zeros uh maybe i’ll just write it out one more time just so you know 000

right remember that so that means of course the zeros are on the right side of the fractional

part and on the left side is going to be 0.110011

1100111 and then now we just have to combine those two numbers so maybe just I’ll put something

here indicating that this is the conversion of just that number like that now we’ll combine

both of those parts right so 45 was this so I’ll say maybe therefore this big number right here

combine this number for 45 and then I’ll just put a decimal point and then I’ll put the fractional

part on the right side and then let me just double check my work real fast it should be

10110111 wait wait what no no 101101 and then 1100111 okay so that’s it we’ve converted

converted a complicated decimal number into binary.

And we can do it in the reverse, just using the same thing.

You know, step one, convert this number into a whole number of decimal.

And then step two, convert this number into a whole number,

sorry, a just only fractional number for decimal

by just getting the one half plus one fourth and so forth.

put them around a decimal point just for practice okay I’ll go ahead and do it

some of you are probably like why won’t you do it I’ll do it okay so just only

looking at the fractional part because that this is not a video to convert

whole numbers in binary and decimal but just to convert the fractional part only

I’m gonna do let’s see say whoops whoops whoops whoops whoops whoops maybe I need

Okay, so starting with just this one right here,

it’s going to be 1 half plus 1 fourth plus not 1 eighth, not 1 16th, a 32.

1 32 plus 1 over 64 plus 1 over 128.

0.8046875.

So it looks like we succeeded.

Okay, so now we know how to convert

a decimal number with a fraction

into a binary number with a fraction.

And we also know how to convert

a binary number with a fraction

to a decimal number with a fraction.

That feels like a long video.

Let’s see what it is after I cut this.

Thank you so much for watching.

I hope you learned a little bit of stuff

and you had a little bit of fun.

I will see you in the next video.

grow this community so we’ll be able to do more videos, longer videos, better videos,

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happens every single time. So you could do it as a nice favor to me or you could troll me if you

want to just wake me up in the middle of the night, just subscribe and then I’ll just wake up.

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The post How to Convert Decimal Fractions to Binary (and Back!) – Easy Step-by-Step Guide appeared first on NeuralLantern.com.

Confused by hexadecimal numbers? Don’t worry! This fun, step-by-step guide makes converting hex to decimal super easy, even for beginners. With clear examples and a chill vibe, you’ll master this computer science skill in no time. Perfect for students, coders, or anyone curious about number systems. Hit subscribe for more coding tutorials, and check out our site for extra resources! #HexToDecimal #CodingForBeginners #ComputerScience #LearnToCode

Introduction to Hexadecimal Conversion 00:00:00
Purpose of Conversion 00:00:11
Number System Basics 00:00:39
Hexadecimal Explanation 00:01:12
Converting Hex to Decimal 00:01:59
First Example Setup 00:02:35
Decimal Place Value Recap 00:03:02
Hexadecimal Place Value 00:05:14
Formula for Conversion 00:05:43
Translating Hex Letters 00:08:17
First Example Calculation 00:09:51
Second Example Introduction 00:11:14
Second Example Conversion 00:11:58
Second Example Result 00:13:11
Conclusion and Call to Action 00:14:00

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Hello there. Let’s talk about converting hexadecimal to decimal.

So why would you do this? Of course, sometimes in computer science and other realms, you may be

faced with a number that looks like this, and it’s got some letters in there, and it’s weird,

and you’re thinking, oops, not a V. That wouldn’t work. Not a G. And you’re thinking like, what does

what does this number mean in decimal well this is a number that is real and we can just change

the way it’s represented uh to decimal so that we can understand what it is so just like a quick

recap if you haven’t watched my other videos yet uh in decimal we have a base 10 system which just

basically means we have these characters zero one two three four five six seven eight nine there

base is 10. In binary, of course, we have base two, which is just, you know, we have a zero and a one

because in the computer, which is why we learn binary, we just have on and off basically for

every single, you know, part of the computer. There’s just like a certain voltage or there’s

not a certain voltage and that’s it. And then for hexadecimal, which is a way to represent the same

numbers, but just in a more compact way. It’s a little bit more compact than decimal. It’s a lot

than binary we can say that this is base 16 which means we have 16 total characters that we can work

with zero one two three four five six seven eight nine and once we run out of numbers we just start

using letters so a b c d e f so there are 16 total characters if we include the zero which means we

So that’s the basics of you know the number basis let’s uh let’s work out how to convert a hex

number to decimal. So I’m going to say ox because in hex when you write down a hex number you should

usually put ox in front of it unless the program you’re working with doesn’t understand that but

usually especially for a human reader you should do it this way. So I’m going to just type like a

few random maybe I have to I have to keep the number small because hex will explode it’ll be

not careful. So I’m going to put like a I don’t know, maybe a few decimal numbers there or a few

like digits that are zero to nine, then I’ll just to make it more interesting, I’ll put some letters

in there. How about like an E there? And then I don’t know, like, we’ll do a B there. Okay, so

how many do I have? 12341234? How about we get rid of? Now, let’s go for it. This is going to be an

So this is our starting number hexadecimal. What we need to do is understand that, well,

a recap if you haven’t watched my other videos yet. In decimal we have, let’s say, 0, 1, 2, 3,

4, 5, 6. You know that the first digit has a strength of 1. You multiply 6 by 1 to understand

the real power of that 6. For the 5, you know that it has a power of 10 or a strength of 10

10 because it’s the next digit over you know to the left same thing for the four it’s like got a

strength of 100 and so every time you move to the left the strength of the digit increases by a

factor of 10. why does it increase by a factor of 10 because decimal is base 10 because we have 10

possible digits we can represent for each character okay so by the time we get to that

left, we have a strength of 100,000. So, you know, if you wanted to really understand 100,000,

if you really wanted to understand, you know, how powerful, let me, let me give some spacing here.

So this feels better. Okay. If you really wanted to understand like, you know, what is the strength?

What is like the actual value of this digit right here? You’re imagining this is like 100,000.

this digit here you’re imagining that this is two of ten thousand you know two times ten thousand

and so forth so uh uh just like another recap the first digit is really 10 to the zero power

like in terms of the strength because if you multiply um let me pin this to the top

if you multiply you know 10 to the something power and you start at zero with the most

the weakest digit 10 to the zero power gives a strength of one and then every time you move over

to the left you just increase the exponent there by one so 10 to the first power is going to be 10

that’s what that five has got so it’ll be five times 10 to give us an understanding of how you

know powerful that digit is move one over to the left it’s 10 to the second power so that’s 100

move one over to the left it’s 10 to the third power and so forth until we get to 10 to the fifth

1 times 10 to the fifth power to understand how powerful that is so we can do the same exact thing

with hexadecimal except instead of raising 10 to a power we raise 16 to a power because hexadecimal

is base 16 whereas decimal is base 10. so that means this e is is uh you know 10 to the or sorry

16 to the zero power and then that 3 is 16 to the 1 power and that f is 16 to the 2 power and so

16 to the 2 power and so forth so first what we should do is let’s write out a

formula which won’t work in a calculator because we’re going to put some letters

in there and then later we’ll translate the letters to actual values so we’ll

start off with the e we’ll say e times 16 to the something power it’s going to be

16 to the zero power okay so then the next digit is 3 so 3 times 16 to the

And then the next thing is going to be F times 16 to the second power.

And just as a reminder here, I’m starting with zero with the smallest digit.

And I’m just working my way up in steps of one.

So it’s zero power or raised to zero and raised to one and raised to two and just so forth all the way to the left.

That number will just keep increasing by one.

The exponent will increase by one.

times 16 to the third power do it again um one times 16 to the fourth power do it again

um d times 16 to the fourth power oh what did i do did i erase something

0, 1, 2, 3, 4, 5.

Oh, that was supposed to be a 5.

Okay, maybe it’s good that I thought I made a mistake

because that drew my attention to the bad exponent.

Okay, so after the D is a B.

B times 16 to the 6th power.

And then one more.

We’ll say 6 times 16 to the 7th power.

And then another one.

A times 16 to the, whoops, to the eighth power.

And another one.

One times 16 to the ninth power.

Ninth power.

Okay.

So just double check your work real fast.

You know, because I make typos all the time and I get things wrong all the time.

So just double check.

Zero, one, two, three, four, five, six, seven, eight, nine.

It’s sequential.

Double check the digits.

6 b d 1 3 f 3 e okay so i got that right i’m not going to erase my work because if i end up screwing

up the next part oh man is it going to be a hassle to correct so i’m just going to copy paste it here

and then i’m going to start translating the letters to numbers anytime you see a number here like one

time something it’s just one but every time you see a letter you have to translate that into

in decimal. Remember in hex, we’ll say, what can I do?

I can say A, B, C, D, E, F.

And I can say that the A is worth 10.

The B is worth 11.

The C is worth 12.

And the D is worth 13.

The E is worth 14 and the F is worth 15.

Well, maybe I should do the other numbers too.

five, six, seven, eight, nine,

just so we have a visual reminder

of like what we’re even looking at.

And I won’t write down what the digits are worth

because they’re worth themselves, right?

So like zero through nine, it’s just worth zero through nine.

So now that we have this little translation table up here,

anytime we see a letter,

we can just translate it very quickly to the decimal value.

So A is worth 10, we’ll put a 10 there.

Maybe I’ll add some spacing so that this continues to line up.

I see a B here, so the B is gonna be worth 11,

11 add another space so it lines up i’m running out of room but i’ll try the d is worth 13 add

another space so it lines up and then the f is worth 15 add another space so it lines up the e

is worth 14 so i’ll add another space so it lines up okay let me just double check my work here a b d

So now I’ve got like a big formula that I wrote out.

I can literally now, I mean, you can do this in your head if you’re like a crazy genius,

but I’m just going to paste this into a calculator and hit enter.

And this is the number that we had originally in hex.

Maybe I’ll put commas here to make things more fun.

I don’t know.

You don’t really need to do that, but I’m going to.

So for me, it’s easier to read.

this is uh like 113 trillion 478 no wait that’s a million and that’s a bill okay so 113 mil a

billion 478 million 25 022. let me punch up my personal calculator here to make sure that i’m

getting this right i’m not going to show this on the screen because i’ve just got this up

on my host machine bet you didn’t know i’m inside of vm right now surprised you didn’t know that

decimal and the number is supposed to be 113478025022 okay so we did this right we now know how

to convert from hexadecimal to decimal and it’s pretty awesome right okay let’s do another number

one that is not quite as hard let’s see how many digits do we have here one two three i think we

5, 6, 7, 8, 9, 10.

Yeah, okay, we had 10.

Let’s do a five-digit hex number.

Okay, maybe I’ll copy…

I’ll copy just this table at the top

since you don’t need it anymore,

but I’m going to need it to do my calculations.

So we’ll do 1, 2, 3, 4, 5,

and I’ll just start randomly changing

some of these numbers.

Like an 8 over here, and how about like a 2?

So I’ve got five numbers.

This is OX.

I’m going to say this is a hexadecimal number.

Kind of ambiguous if we tell the reader this is a hex number,

but then we put OX.

Kind of don’t really need to tell them that it’s hex

because OX tells you it’s hex.

It’s not even part of the value.

So let’s get on with it.

I’ll start by just doing 8 times 16 to the something power,

which is going to be 0 for that first position.

the power as we go to the left so it’s going to be 1 times 16 to the first power and then it’s

going to be f times 16 to the second power and then it’s going to be 2 times 16 to the third

power oh no my thoughts are wandering i think i’m getting bored of recording this video i’m starting

to the fourth power but honestly why couldn’t they end up together so and

then I think one two three four five okay so that’s five digits a to f one

eight a to f one eight all right zero one two three four just to make sure

that I got my exponents right copy paste it so I don’t have to repeat my work if

I get something wrong I’m gonna translate the letters into numbers so a

becomes 10 f becomes 15 and the other numbers are fine as is I can just copy

fine as is I can just copy paste this whole thing stick it into a calculator and now I know that

this number is actually 667 416 with a little comma in there don’t put commas if you are taking an

exam somewhere if you’re watching my video to help with your exam because most most likely the exam

that you’re taking will not accept a comma it’s not been pre-programmed for a comma I don’t know

If you start typing numbers and a comma just shows up, then it probably was programmed for a comma.

But don’t assume it might be a string match and not a numeric match.

So be careful out there.

Be careful.

So 667-416.

Let me punch this into my personal calculator just to make sure I got this right and I don’t have to issue an errata.

667-416.

All right.

We’ve done it.

We know how to convert hexadecimal numbers into decimal numbers.

Thank you so much for watching this video. I hope you enjoyed it and had a little bit of fun and

learned a little bit of stuff. I’ll see you in the next video. Hey everybody, thanks for watching

this video again from the bottom of my heart. I really appreciate it. I do hope you did learn

something and have some fun. If you could do me a please, a small little favor, could you please

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That’s exactly what happens every single time.

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wake up I promise that’s what will happen also if you look at the middle of

the screen right now you should see a QR code which you can scan in order to go

to the website which I think is also named somewhere at the bottom of this

video and it’ll take you to my main website where you can just kind of like

see all the videos I published and the services and tutorials and things that I

for clarifications or errata or just future videos that you want to see please leave a comment or if

you just want to say hey what’s up what’s going on you know just send me a comment whatever I also

wake up for those in the middle of the night I get I wake up in a cold sweat and I’m like

it would really it really mean the world to me I would really appreciate it so again thank you so

much for watching this video and enjoy the cool music as as I fade into the darkness which is

the darkness which is coming for us all.

Thank you.

The post Hex to Decimal Made Easy: Fun & Simple Conversion Guide! appeared first on NeuralLantern.com.

Hey there! Struggling with binary to hex conversions? This video makes it SUPER easy—no math required! Learn to convert between binary and hexadecimal with simple patterns you’ll memorize in no time. Perfect for computer science students, coders, or anyone curious about how computers work. Subscribe for more tutorials, and scan the QR code to visit my site for extra resources. Drop a comment with your questions or video ideas! #Binary #Hex #ComputerScience #Coding

Introduction to Binary and Hex Conversion 00:00:00
Why Convert Between Binary and Hex 00:00:13
Recap of Number Systems 00:00:41
Binary Base Two System 00:01:01
Hexadecimal Base Sixteen System 00:01:24
Benefits of Hexadecimal 00:02:06
Simplifying Binary-Hex Conversion 00:03:04
Four Bits Equal One Hex Digit 00:04:32
Memorizing Binary-Hex Patterns 00:05:13
Creating a Binary-Hex Conversion Table 00:06:26
Converting Hex to Binary Example 00:08:52
Understanding Nibbles and Bytes 00:10:44
Converting Binary to Hex Example 00:13:19
Conclusion and Verification 00:15:38
Call to Subscribe and Engage 00:16:20

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Hi there! Let’s talk about converting back and forth between binary and hexadecimal.

Why would you want to do that? Well, maybe you’re in computer science. Maybe you’ve been presented

with some numbers that you need to convert. Maybe you have like a bunch of ones and zeros.

Maybe you have like an ox and then something that looks really weird. It’s got some letters in it,

but it’s also got some numbers. And you’re trying to figure out what are these? What are we trying

we try to convert back and forth between.

You should have watched my other videos by now,

which will teach you how to convert back and forth

between both of these number bases and decimal.

So you can understand what they are

in just normal human terms.

But as a quick recap, decimal is a base 10 number system

because we have 10 possible characters that we can use.

We can say zero, one, two, three, four,

five, six, seven, eight, nine.

So that’s 10 total characters, zero through nine.

We also have binary, which is what computers use, which is a base two system.

It’s base two because the only characters you have available are just zero and one.

So base two, two characters.

You can represent a number between zero and one in a single digit.

Then we have hexadecimal, which is a way to represent a number in a more compact way.

system there because we have 16 possible characters we have 0 1 2 3 4 5 6 7 8 9

just like decimal but then we add more numbers we had like six numbers we say

a b c d e f and what happens is the a has a strength of 10 whereas the you know

the 9 just to its left had a strength of 9 the a has a strength of 10 the b has a

of 11 the c has a strength of 12 and the d has a strength of 13 and the e has a strength of 14

and the f has a strength of 15 and so you know we just have more characters that we can use in one

single digit which means we can rent we can represent the same number in decimal but just

we can represent it smaller if we use hexadecimal so it’s kind of useful when you’re working with

looking at bits in binary or hex and not necessarily decimal because binary as

you’re going to learn in this video gives you kind of a good idea just by

looking at it after you’ve practiced a little while gives you a good idea of

what hex numbers you would be seeing if you were looking at the same number and

vice versa if you’re looking at hex numbers if you look at them a lot in

your daily life you’ll start to kind of like see through the matrix and you’ll

And if you’re interested in finding what bits are on and off,

it’s convenient to be able to look at a hexadecimal number

and kind of intuitively know,

okay, those bits are probably like on and off.

Those bits are all on, you know, whatever.

So this is the basics of number basis.

Here’s a trick.

In all my other videos,

when we converted back and forth

between decimal and binary and hex and all that stuff,

we used multiplication, we used division,

you know, we messed with the numbers quite a bit.

the great thing about binary and hex conversions is you don’t even really need to do math.

Maybe a little math at first while you’re learning, but eventually when you get used to it,

you start to realize you can memorize short patterns. Let me bring your attention to the

fact that in hexadecimal, you have 16 possible combinations, or you can represent a number

you can do the same thing in four characters if I had four characters right

here in binary very quickly you could do the calculation in your head if you’ve

watched my other videos you can see well that one counts for a one and this one

counts for a two and this one counts for a four and this one counts for an eight

if I want to know what the maximum value is that I could represent with four

digits I just take the the top numbers strength multiply it by two and then

strength multiply it by 2 and then subtract 1. So if we have 1, 2, 4, 8, I’ll just multiply 8 by 2,

that’s 16, and then subtract 1, that’s 15. So I can represent a number between 0 and 15 with 4

binary digits. But I just said you could do that with one hexadecimal digit, right?

So that means one hexadecimal digit is actually four binary digits. And if you just memorize

16 combinations of numbers, which is not like that hard.

And even if you don’t memorize them all,

I don’t have them all memorized.

It’s really easy to convert in your head

a four digit binary number to decimal

and then convert that back to hexadecimal pretty fast,

hexadecimal.

So what’s the equivalent of 1111?

Well, we know it’s the highest possible value

with just one hexadecimal digit.

So that would have to be an F.

So you can memorize already

You can memorize already a couple of really, really easy combinations.

We could say, let me say zero binary, OB to say that we’re looking at binary is equal

to zero X F. So just the letter F in hex.

Remember that we like to prefix different base number systems to give the reader a reminder

of what base they’re looking at.

one i’m going to say that 000 in binary is just zero in hex if i didn’t put that prefix how would

you know if you’re looking at hex or binary or decimal it would be even more confusing if you

had like you know one two zero is that hex one two zero or is that uh decimal one two zero i guess it

can’t be binary one two zero but if we did one one zero now it could be binary or hex or decimal so

i’m just going to put uh zero b for binary and i’m going to say it’s zero so that’s two of the

of the 16 total possible combinations that we would memorize.

So let’s iterate through all the combinations.

Just for the sake of making this table more compact,

actually, let me start a new little notepad page here.

I’m going to omit those prefixes because those are a good idea,

but while we’re doing our lookups, they’re a little irritating.

So I’m going to take them out.

So I’m going to say 0001.

Let me say this.

So I’m just going to count from 0 to 15 in binary.

to 15 in binary.

So this is going to be one, one,

and then zero and then zero, one, zero, one, zero, one,

I don’t know, that’s a lot of copy pasting.

Let me just double check here that I’m doing this right.

I should have 16 lines.

I don’t, so I’ve done something wrong.

Let’s see.

So this is like 0, 1, 2, 3, and this is 4.

This is 5, and then 6, and then 7, and this is 8.

Oh, I have that twice.

Okay, 8.

And then since I copy pasted the bottom part,

I think I can probably assume that’s okay.

One, two, three, four, five, six, seven.

That was kind of spooky.

I guess a lesson learned is that relying on a battery pack

or a light that’s gonna stay on for many hours

is probably a dumb idea.

Anyway, continuing, we have this table here.

We have like 16 possible combinations.

So now I’m gonna map these to hexadecimal digits.

uh you know like 10 are going to be really easy right it’s just going to be zero and then one

and then two you can make a vertical table if you want for yourself I’m just doing it this way

because it’s easier the way that I’m typing in this notepad the way that I’m typing in this

notepad so I’m going to do seven eight nine and then when we get to 10 let me just double check

10. So this is eight plus two. So that means this is indeed a 10 and oh, 10 in hex, not a decimal.

So that’s a and then B and then C and then D and then E and then F. Okay. So now that we have this

little table set up, you know, if you want to write it horizontally, that’s fine. It’s actually

binary and hex now imagine we have a gigantic hex number zero x and then i’m just going to do like a

bunch of numbers and then i’m going to do change some of these to like letters just to make things

more interesting a b c d e did i use any d e f e b i didn’t use a b oh there we go and i’ll put like

another aid in there okay so this is huge and this would take like a while to calculate right

to calculate right if you were going to convert it to decimal for hex to binary conversion it’s

actually pretty easy you literally just go b what is b b is that so b is just that you don’t even

have to do any math let me copy paste this down here so i can show you a really easy way to do

D is this right here.

So I’m going to say the D is that.

And then the 6 is that pattern right there.

So move you over.

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4.

Maybe that’ll line up later, hopefully.

So the 1 is pretty easy.

Probably didn’t even need to copy-paste that.

I could have just looked at it and typed.

looked at it and typed the E is going to be that and the seven is going to be that

and the two is going to be this eight see what I’m doing I’m literally just

copy pasting the bit patterns if you don’t have copy paste when you’re doing your conversion

that’s okay you can at least write down zeros and ones really fast if it’s just

you know four at a time I should also point out that um you know this is pretty important to

good term that people like to use. Four bytes or one hexadecimal digit, it’s called a nibble.

So usually you’re used to seeing eight bytes in a row and you call that, sorry,

usually you’re used to seeing eight bits in a row and you call that a byte or two hex digits in a

row and you call that a byte. If you just see four bits or one hex digit, that’s a nibble.

Two nibbles make a byte. Try to remember that. So we have this giant thing here.

we have literally now successfully converted binary.

I’m going to put, I’m just going to put OB here

and then remove all the spaces.

This is the binary number that we originally had

in hexadecimal.

So again, just to emphasize, these are the two same numbers.

They’re just represented differently.

Differently.

Let me punch this into my personal calculator

to make sure that I gave you the right walkthrough

so I don’t have to correct in a video later.

so expression X result binary oh god I can’t even I can’t even read that okay

so let me let me do it backwards I’m gonna copy paste this one in there okay

so let’s see X okay so it’s telling me that supposed to get to B and then a D6

728fac. Okay, so I did it. And this is also a good reminder that you kind of want to pair off

into groups of one byte at least. So, you know, each two characters, that’s one byte. One character

by itself is a nibble. So you want to pair off into bytes. And notice how this b is all by itself.

So you want to pad to the left with a zero so that you’re just kind of working with bytes.

It’s easier on the eyes and the brain. And you’ll usually see something like this

output from a program or something. In fact, you might see something like this representing,

here’s a word, or you might see something like this showing that this is like a D word or,

you know, like a 32 bit number. And if we wanted to say, oh, this is a 64 bit system. So let’s

look at 64 bits. Let’s look at eight bytes. Then we’ll just like pad it with, let’s see, one, two,

that’s one, two, three, we’ll pad it with a bunch more zeros. One, two, three, four, five, six,

So this is a proper 64-bit number or an 8-byte number that works with modern systems,

whether you have the space in there or not.

And so I’m not going to do another example from hex to binary.

Let’s do a quick example from binary to hex.

It should be just as easy.

So I’m going to start a new tab here and just copy-paste the table that I made.

Let’s make a bunch of random numbers for binary.

And so now we’ve got like a bunch of numbers.

All we have to do is I’m going to copy paste this so I don’t ruin the original thing that

I wrote down.

And I’m just going to break it up into groups of four, starting from the least powerful

digits, you know, like all the way on the right.

So I’m going to go doop, doop.

Okay.

So after breaking it into groups of four, you can see that the, you know, the most powerful

digit there is a one all by its lonesome.

I could put 000 to make sure that they’re all groups of four bits. I don’t really have to because

I could still kind of understand just by looking at the one that it’s going to end up being a one

and then literally just translate it the same way I did before. Okay that’s a 1.

1 0 1 0 that’s an A. What’s a thousand and one? It is a nine. What’s a 0 100?

what’s one oh one oh a what’s a thousand and one didn’t i just do that that’s a nine

what’s a zero zero oh ten that’s going to be a two for sure yeah two i finally got one off the

top of my head one zero one one that’s a b and then uh basically 15 minus eight i don’t really

want to work that out of my head right now so i’m gonna look at the table seven okay i guess i

should have done that easy right like how fast was that so i’m just going to copy paste these

put an ox in front of it and maybe bunch them into groups of two first to see what’s up

okay so they’re not in groups of two that means this one is kind of i should have started grouping

them on the right side kind of messed it up someone just you know rearrange the grouping

Let me punch this into my personal calculator to make sure that I got this right. Actually, let me do this original number here

I must say

This binary number is supposed to be

1 a 9 4 a 9 2 b 7. Okay, we did it

Really easy, right? So every time you have to convert back and forth between binary and hex

It’s your lucky day because that’s like one of the easiest conversions you could do

Thanks for watching this video. I hope you learned a little bit of stuff and had some fun

I’ll see you in the next video.

So we’ll be able to do more videos longer videos better videos or just I’ll be able to keep making videos in general

So please do do me a kindness and and subscribe

You know sometimes I’m sleeping in the middle of the night

And I just wake up because I know somebody subscribed or followed it just wakes me up and I get filled with joy

That’s exactly what happens every single time

So you could do it as a nice favor to me or you could you control me if you want to just wake me up in the middle

And I just subscribe and then I’ll just wake up. I promise that’s what will happen

that’s what will happen also uh if you look at the middle of the screen right now you should see a

qr code which you can scan in order to go to the website which i think is also named somewhere at

the bottom of this video and it’ll take you to my main website where you can just kind of like see

all the videos i published and the services and tutorials and things that i offer and all that

good stuff and uh if you have a suggestion for uh uh clarifications or errata or just future videos

future videos that you want to see please leave a comment or if you just want to say hey what’s up

what’s going on you know just send me a comment whatever i also wake up for those in the middle

of the night i get i wake up in a cold sweat and i’m like it would really it really mean the world

to me i would really appreciate it so again thank you so much for watching this video and um enjoy

the cool music as as i fade into the darkness which is coming for us all

Thank you.

The post Binary to Hex Conversion Made EASY! No Math Needed! appeared first on NeuralLantern.com.

Want to master decimal-to-hexadecimal conversion? Join me in this fun, beginner-friendly tutorial where we break it down with clear examples?like turning 223 into 0xDF! From number systems to handy calculator tricks, I?ll guide you step-by-step, no stress. Bonus: my dog makes a cameo! Perfect for coding newbies or anyone curious about hex. Subscribe for more easy tech tutorials, and let me know what you want to learn next! #DecimalToHex #CodingBasics #LearnToCode

Introduction 00:00:00
Number Systems Overview 00:00:12
Decimal vs. Hexadecimal 00:00:39
Hexadecimal Digits Explained 00:01:06
Conversion Process Introduction 00:01:40
First Conversion Example Start 00:02:10
Handling Remainders 00:02:38
Dog Interruption 00:03:16
Continuing First Conversion 00:03:43
Finalizing First Conversion 00:06:04
Reversing Digits Order 00:06:24
Mapping Numbers to Hex Letters 00:07:34
Verifying First Conversion 00:08:48
Hexadecimal Prefix Importance 00:10:57
Second Conversion Example (223) 00:11:34
Third Conversion Example (2816) 00:13:32
Hex and Binary Relationship 00:14:56
Padding Zeros in Hex 00:16:07
Video Conclusion 00:16:58

Thanks for watching!

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Hello there.

Let’s talk about converting decimal to hexadecimal.

Hopefully you’ve watched my other videos by now, but basically we have different number

systems, number bases that we can use.

We have decimal, which is a base 10.

which is base 10 or sorry base 16.

We can basically convert back and forth between all of these systems.

We can represent the exact same number just in different ways.

Just as a quick refresher.

Decimal, we can have characters that are 0 through 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

That’s 10 total characters.

That’s why it’s base 10.

In binary, we have, you know, just characters 0 and 1.

characters 0 and 1 and in hexadecimal it’s meant to compact the representation a little bit it has

more characters or more possible characters per digit than decimal so the number is going to be

a little bit shorter usually unless it’s like very very small than decimal and it’ll be a lot shorter

than the same number in binary so in hexadecimal we start off with 0 1 2 3 4 5 6 7 8 9

three, four, five, six, seven, eight, nine.

And then to get the remaining digits, we just go A, B, C, D, E, F.

So we have this many characters.

It’s 16 total characters.

We can represent a number between 0 and 15.

So that’s a difference between, you know, hexadecimal and decimal.

Now let’s learn how to actually convert.

So I’m going to start off with a number.

I’m just going to type like a random number here.

Hopefully this doesn’t go on for too long, the conversion.

decimal number is just that. How do we convert? If you watch my other videos, it’s basically the

same thing as converting from decimal to binary, except instead of dividing by two, because binary

is base two, we’ll divide by 16 because hex is base 16. So I’m going to start off by saying,

let’s take the original number and we’ll divide it by not two, 16. What does that equal? There’s

no way I’m doing this in my head. So I’m just going to use a calculator for every single step,

going to use a calculator for every single step not even going to try I’m

going to say this number divided by 16 is 5 1 1 7 5 7 with some sort of a

remainder so I’m gonna go 5 1 1 7 5 7 remainder something so in most

calculators you can just punch up the modulo operator which is like the

percent symbol before I do that I just want to point out 0.75 is 3 4ths of

of whatever it is that is one you know that one character can represent we know

we can represent 16 different values what’s 16 divided by 4 that’s 4 so three

of those should be like 12 I hope unless I’m saying something totally wrong so

I’m gonna do modulo so that’s 12 okay remainder 12 my dog is growling at me

He likes to lie about peeing.

He doesn’t actually pee.

He already did a huge pee and then three times after that at 20 minute intervals, he went

out there and lifted his leg and just like three squirts came out and he expected a giant

treat for it.

I’m not doing it.

You’re not getting that treat.

I expect a big pee pee if you want a treat.

You dog?

Dang little dog.

Okay.

So, here we are still dividing.

here we are still dividing. I got the remainder. So then we just need to take, you know, the

quotient result, you know, what is the result of actually dividing, just carry it over to

the next line. I’m going to do some spaces to make it look all even and continue to divide.

So divided by 16 equals something. Don’t forget that if you have the modulo operator over there,

you got to take it out, go back to division. It’s going to be 31984 remainder something.

what’s the remainder i’m just going to get the modulo i don’t want i don’t want to recall what

0.8125 is i’m sure some of you out there can already do that but it is 13 remainder 13.

um so i’m gonna go 319 divided by 16 31984 divided by 16 so it’s going to be 1 999 okay so carry that

over real fast though divided by 16 equals 1 9 9 remainder something there’s no decimal point at the

There’s no decimal point at the end of that so I can just assume the remainder is going to be zero.

If you want to double check to be sure, which is a good idea, use the modulo operator.

If your calculator doesn’t have modulo, find another calculator or jump into Python or something.

So I’m going to carry over 199 to the next line there.

1, 2, 4, remainder, whatever modulo says, 15.

That’s pretty cool.

All right, then I’m gonna carry it over,

just 1, 2, 4, divided by 16 again.

If you were hoping I’d be able to do it in my head by now,

you were wrong.

1, 2, 4, divided by 16, it’s gonna be 7.75,

so just like seven, remainder something.

What did I say last time for the 3 4ths?

Was that 12?

whoops, I can’t remember anymore.

12, yeah, okay, so remainder 12.

And then we’ll carry it over and we’ll say 7 divided by 16.

So we know that, you know, 16 doesn’t really fit into 7 at all.

So it’s going to be 0 remainder, whatever the number is.

Let’s punch it here just to double check.

We’ll say 7 divided by 16.

You can see that it’s 0.

And then the remainder is going to be 7, just, you know, what the original number was.

number was. So now at this point when the actual you know carry down quotient is

going to be zero then we just have zero divided by 16 equals just zero remainder

zero and it’ll just continue like this forever and ever and ever and ever and

ever. So this is how you know you’re done. Another thing that I mentioned in

other videos is how do we actually know where the zeros belong? I mean if you

read this intuitively from the top to the bottom you might think that you know

you know the top number is going to be like the first digit but it’s actually

backwards it goes from the bottom up the reason you can know that is again based

on my other videos if we just type a random decimal number here if I add

zeros to the right side I’m actually changing the value of the number I’m

making it bigger but if I add zeros to the left side I’m not changing the value

at all so that means those zeros here which could go on for infinity based on

how much tenacity you have they should be on the left side because you don’t

side because you don’t want any amount of these zeros to change the value of your number because

they you know it’s an arbitrary number of zeros based on how how fast you get tired of doing zeros

so that means if i go from top to bottom i have to reverse it if i go from bottom to top it’s

already going to be in the right order or sorry if i if i correlate or if i map bottom to top to mean

left to right then it’s fine already if i map top to bottom for left to right then i’ll have to

For left to right, then I’ll have to reverse it when I’m done.

So I’ll do it both ways just to show you.

But there’s one more step we need to do because in hexadecimal,

we have more characters than decimal.

We have to translate what does this 12 and 13 and these other numbers mean.

Luckily, we had some of them in there.

It could have been too easy.

So remember in hex, we have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

And then we have A, B, C, D, E, right?

So we know that the value of 0 is 0 and 1 is 1 and 2 and 2 and so forth, right?

Like 9 is 9.

But what’s the value of A?

For each increasing digit, the value just goes up by 1.

So that means that A is worth 10.

I’m going to write this vertically just so that you understand that this means the strength

of the A is 10.

And then the strength of the B is going to be 11 because it just increases by 1.

The strength of the C is 12.

The strength of the D is 13.

Oops, I forgot the F.

Oops, I forgot the F. Hit F in the chat if you forgot the F too.

So the strength of the E is 14. The strength of the F is 15.

And then we’re done. And remember, there’s 16 digits total.

So the highest value is 15 because it includes the zero.

So, you know, 16 total possible values you could represent, but the highest value, 15.

So that means every time we see a 12 here,

say that that’s really a C and every time we see actually let me let me put

the other C in there real fast every time we see a 13 that means it’s a D

every time we see a zero zero through nine it just it means the original

number oh wow we only had two digits that are gonna mean the original number

so mark my words you know the 15 is gonna be an F every time you see zero

one two three four five six seven eight nine it maps to the same number so seven

maps to seven it’s totally fine the only time it maps to a letter is of course when you exceed nine

so 10 and above are going to map to letters so now i have these mappings i just need to sort of scan

uh my my work to come up with the correct hexadecimal number so i’ll start from top to

bottom because it’s a little bit harder that way and it’ll be more brain practice i’m going to go

and then you know as many zeros as you decided to calculate and hopefully this

reminds you oh no I’m increasing the value by adding the zeros that means I

have to reverse everything so I’m gonna get rid of these zeros though and I’m

gonna reverse it 7cf0dc okay great now let’s double check because it’s always

a great idea to check your work in different ways with different methods to

decrease the possibility that you’re accidentally wrong so now I’m gonna go

So now I’m going to go from bottom to top and see if it’s the same thing.

7 C F 0 D C. Does it match? Yes.

So now I’m pretty confident that I have the right answer.

Let me punch this up in my personal calculator real fast.

I’m going to do just to double check the work before we cut the camera,

because if I’m wrong, I want to be able to correct myself right away.

Instead of coming back with another video later,

which sometimes I guess I’ll have to do.

f0 dc is the correct answer all right so we now have converted our first number from decimal to

hexadecimal nice and by the way if you didn’t already know this you’re supposed to put a

prefix in front of hexadecimal numbers not necessarily in every program that asks for

hex input some of them are not programmed that way but in general when you expect someone to

read your numbers if it’s hex you want to put ox in front of it because you don’t want them to

confuse, let’s say we have this number and this number and this number. All three of those could

be a different number depending on whether they’re binary or decimal or hex. But if you put the

symbols in front, this is binary, this is hex, then now the reader knows that these are three

different numbers and they can infer what the numbers mean. Okay, so let me, let’s just do like

another number. We’ll make it a little bit smaller so it’s easier. We’ll say decimal and we’ll go two,

and we’ll go 2 2 3.

So it’s faster.

So we start off with 2 2 3,

we divide it by 16,

and that’s going to be something.

So 2 2 3 divided by 16

is going to be 13 remainder something.

I’m going to do the modulo operator.

And by the way,

if you don’t have a modulo operator

and you can’t figure out a better way to do this,

a good trick is to just say,

let’s take 13,

because that was the answer, right?

13 point something.

We’ll take 13 and multiply that by 16 again,

that by 16 again so it goes higher then take the difference between that and the original number

so we can say 223 minus uh the number multiplied back up and it’ll tell us that our remainder is 15.

let’s see was that actually the remainder let me just double check here oh gosh what am i doing

223 modulo 16 15 yeah there it is if you’re lazy like me you could also do something like this i

and I don’t have a modulo.

I’ll do 13 times 16 and it’s 208.

And then I’ll just subtract the original number

and then we get negative 15,

but then I know it’s not negative, I know it’s 15.

So it’s just like, it makes you a little bit faster

in the calculator.

So this number I think was too small

because we just do 13 and then divide that by 16.

Obviously the answer is gonna be zero remainder 13.

And we just have a two digit hexadecimal number.

digit hexadecimal number. Let’s do that real fast. What is 15 going to be? It’s A and no, no,

no, not A. Sorry. That’s F. Subtract two from that. D E F. So it’s going to be D, I think.

So then if we go from bottom to top, it’s going to be O X D F. Let me double check that I’m

telling you the right thing. 223 D F. Okay. So we got it right. Let’s do something just like a

not as difficult as the first one so I’ll try four digits maybe two two two two

how about that four digital four digital digits how about that we’ll do

two eight one six divided by 13 equals something two eight one six divided by

16 that’s 176 remainder something there’s no decimal point so I can just

16 is 176 divided by 16 is 11.

Another zero remainder.

Getting kind of boring though, isn’t it?

Remainder zero.

And then we’ll do 11 divided by 16.

That’s going to be zero remainder 11.

That’s too easy.

Okay.

So what is zero?

Zero is zero.

You’re welcome.

And then what is zero?

It’s also zero.

0, it’s also 0 and then what is 11? That’s B.

So we should have a number now of 0xB00 if we’re going from the bottom to the top.

If you go from the top to the bottom of course it’ll be 00B and then you reverse it B00

but I just wanted to skip that step for now.

Let me punch this up into my personal calculator to make sure I don’t need to make a correction.

B00, there we go.

Also, you know, here’s another thing to keep in mind.

it’s to read you know sets of bytes which typically go in patterns of one byte or two

bytes or four bytes or eight bytes or whatever so the cool thing about hex is one character

can represent a number from zero uh to 15 or 16 combinations and if you think about that in binary

that’s four bits right it’s like one two three four one two four eight multiply eight by two

16 subtract 1 is 15.

So you can go from 0 to 15.

So that means for every character in hex,

you get four characters of binary.

So it’s like a huge savings, right?

But the point is, if you wanted to represent one byte,

that’s not going to be four bits.

That’s going to be, you know,

four bits followed by four bits for a total of eight bits.

Even if there are zeros in the beginning,

in binary, if you’re representing a byte,

But in binary, if you’re representing a byte, you typically want to pad the zeros to the

left so that it looks like it’s aligned to nice blocks of eight or 16 or 32 or 64 in

terms of bits.

So we should do the same thing with hex.

We should always have two hex digits together.

We should try not to have like an odd number of hex digits.

And if you want to get more strict than that and say like, oh, only, you know, two or four

eight you can do that but i just will say pad it with a zero to the left remember when you pad a

number with zeros to the left it doesn’t change the value like if i just put a bunch of zeros in

front of this decimal number it wouldn’t change the value so we can do that with hex and it looks

nicer and neater and people can quickly see okay so there’s like a byte right there it’s ob

they can imagine oh that byte is probably um 11. so there’s like a like an 11 byte it’s like got

a sequence of zeros and ones and then there’s another byte right after it which is smaller

which is smaller, which just has zeros.

So it just helps the reader visualize what’s going on.

Okay, I’m going to cut the video here.

I hope you enjoyed this video.

I hope you learned a little bit of stuff and had a little bit of fun.

I’ll see you in the next video.

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