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

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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,

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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

Thanks for watching!

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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

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.

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 of the night just

subscribe and then I’ll just wake up I promise that’s what will happen also if

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 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.

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

subscribe and follow this channel or these videos or whatever it is you do on the current social

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.

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.

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 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

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That’s exactly what happens every single time

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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

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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.

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.

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please a small little favor could you please subscribe and follow this channel

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And I just wake up because I know somebody subscribed or followed.

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That’s exactly what happens every single time.

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Thank you.

The post How to Convert Decimal to Hexadecimal: Fun & Easy Guide for Beginners appeared first on NeuralLantern.com.

Binary got you baffled? Let’s break it down! In this fun crash course, I’ll show you how to convert binary to decimal step-by-step—super easy, no stress. We’ll go from 765,432 in decimal to 10101111 in binary (that’s 335, btw), with tricks to eyeball it fast. Perfect for beginners or anyone who loves a good tech challenge. Hit subscribe—I wake up in a cold sweat when you do, and it means the world! More vids coming your way!

Introduction to Binary and Decimal 00:00:00
Understanding Decimal System 00:00:44
Decimal Position Strengths 00:01:39
Decimal Formula Explanation 00:03:48
Transition to Binary System 00:06:31
Binary Position Strengths 00:07:19
Binary Formula Breakdown 00:10:46
Calculating Binary Example (335) 00:12:55
Quick Binary Conversion Trick 00:15:24
Memorizing Binary Positions 00:13:52
Small Binary Example (19) 00:15:43
Closing and Subscription Request 00:16:48

Thanks for watching!

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Hello there. Let’s talk about converting binary to decimal.

Just a quick recap for those of you who don’t know. Watch my other videos if you’re not sure

about number bases, but basically, you know, decimal is a number system that has 10 characters

to represent a number. So 0, 1, 2, 4, 5, 6, 7, 8, 9. That’s 10 characters in decimal.

In binary, we just have two characters.

So it’s base two, whereas decimal is base 10.

How can we convert between the two?

Well, first, before we can try to convert between the two,

we should try to understand what’s really going on with normal decimal representations.

So if I have a decimal number here, and I say, I don’t know,

let’s just type a couple of random numbers.

How do we really know what this value is?

How do we kind of understand what is the meaning?

Okay, so you know that, you know,

if you just kind of look at this for a second,

you’ll realize this is 765,000, right?

765,432.

How do we know that this is 700,000?

Because it’s in a certain position.

It’s like, you know, several digits to the left.

How do we know that the next one represents 65,000?

Well, it’s one less to the left.

uh it’s a tenth of the like power of the seven digit same thing for the five how do we know

that’s a thousand same thing for the four and the three and the two what we really do is we end up

deciding okay you know what the uh the first digit here on the right side that two uh the strength of

of one. So like, you know, two times one is just two. So whatever, whatever that digit is, if it

was a five, it would just be a five, five times one is five, right? So the strength of the very

first digit on the right side is just one. Every time we move one digit to the left, we multiply

the strength by 10. The reason we multiply the strength by 10 is because there are 10 possible

digits, or 10 possible characters that we can use in decimal. Makes sense, right? So that means the

Makes sense, right?

So that means the three, we know that represents, you know, an addition of 30 because that’s

the 10th strength place.

Same thing for the four.

We multiply 10 by 10 again to get 100 in that position.

So this one has a strength of 100.

I’m writing this vertically.

Hopefully this is not too messy, but I’m hoping you’ll understand.

Well, I don’t know.

Maybe if I space this out, does that make it better or worse?

maybe it makes it slightly better i don’t know i’m going to roll with it

what can i say i’m a rebel okay so i live dangerously the five we know that’s worth

five thousand because again the four position over here you know that third digit it had a

strength of 100 so we multiply that strength by 10 going to the left to to end up with a thousand

to end up with a thousand.

So same thing with the six.

I’m not going to explain that any further.

You know, it’s got a strength of, you know, 10,000.

Okay.

And then the seven, it’s got a strength of 100,000.

And it just keeps going and going and going to millions and billions and trillions

and however far you actually want to go.

That’s how we understand the decimal numbers

that we’re looking at.

How could you imagine this in terms of a formula?

Well, we’re really raising something to the 10th power.

If you think about this, the one,

we could imagine that the value one

is actually 10 to the zero power

because anything raised to the zero power is just a one.

Let me pull up this calculator real fast.

I got to stick that on my desktop in the future.

If we say 10 to the zero power, it’s just one.

Any number to the zero power is just one.

Okay, so then we would multiply that strength

by the actual digit that we see,

the character that we see.

It’s a two.

Okay, so that’s going to be two times 10 to the zero power.

I’m going to put that in parentheses

to keep it a little bit clean or somewhat cleaner.

So now when we go one to the left

to look at that three digit,

to look at that three digit, we end up with three times something.

Let me get a space here for my brain.

Times 10 to the something power.

Well, every time we go to the left, we just really have to increase the power by one.

It’s 10 to the first power because we’re looking for actually just the number 10.

So if we say 10 to the first power on that calculator, it’s 10.

So then, you know, just keep repeating the process.

10 to the second power. And that should be 100. So if I say 10 to the second power, it’s 100.

All right. And, you know, we’re adding all the positions together, even though we’re multiplying

the digit by its strength. So I’m going to say five times 10 to the third power. And then again,

just to double check here, 10 to the third power is 1000. So you can see the five was supposed to

and then again we’ll say six times ten to the fourth power and then just double check here

the fourth power should be a thousand sorry ten thousand and then we’ll do it one last time we’ll

say seven times ten to the fifth power which should be a hundred thousand all right so now

that we’ve written this all out you know this is kind of madness right what you can do now

do now is you can put this into the calculator and it should give you the exact same number that

we started with. We should see 765432, unless there’s a typo. 765432. Nice. Okay, that might

have seemed like it was a little bit of a waste of time, but it’s not because now we kind of

understand the breakdown of the different positions of the digits in decimal, which means

now we can do the same thing in binary, basically the exact same thing, except just use a power of,

use a two to some power rather than a 10 to some power because the only reason we use 10 down here

it says we were in decimal that has a base of 10 now let’s go into binary

which is um a base of two so i’m going to just i guess maybe what did i do wrong

i hit something and it like did a space i don’t even want to know i don’t even want to know

okay so let’s do a binary number i’m just going to type a few random digits

a few random digits. I don’t know what number this is yet, but let’s work it out slowly

in the same way. You know what, maybe instead of doing the formula first and only, let’s do

both parts like we did with decimal. So what’s the position, what’s the strength of the position

for that first character? Well, I said before the first character is always just going to be,

sorry, the first digit is always just going to be a one, right? That’s going to be true

So I’m going to say this has a strength of 1.

How do we know it’s a strength of 1?

Because we’ll take 2 to the something power.

We start at 0 for that first position, and it’s going to give us a 1.

Okay.

So the strength of this one, I already know binary.

So I just know off the top of my head that to go to the left,

the strength just multiplies by 2.

And that’s pretty easy after you start memorizing it.

I haven’t quite memorized hexadecimal yet, but maybe you will in another video.

So I’m going to multiply one by two and I’m going to end up with two.

Double check over here in the calculator.

Two to the first power is two.

So then the strength of this next digit should be four.

Two times two is four, right?

So let’s do two to the second power.

That’s four.

Multiply by two again.

It’s going to be eight.

Double check over here.

Two to the third power is eight.

The next digit is going to be 16 of its strength.

So I’m going to write this vertically again.

So it’s going to be 16.

Double check over here with the calculator.

Double check over here with the calculator, 2 to the 4th power is 16.

Next digit is going to be 32.

Double check with the calculator, 2 to the 5th power.

And things are starting to get messy, so I think I’m going to like space everything out probably.

Just to make it easier to read.

Tell me if you think this makes it actually easier to read or if I’m making it way harder.

I think I’m making it easier.

Okay, so we got 32.

two. Next one up is going to be 64. Just multiply it by two. Double check two to the sixth power.

That’s going to be 64. And then the biggest one that we’ve written down is going to be 128.

Double check it. Six to the seventh power is 128. We could go on and on and on, but I’m just going

to leave it here because we, I hope we have a pretty good idea of, you know, what this means.

delineation or like a delimiter showing us that these are just representing the strengths and

this is the actual number. Okay, so how can we write this out in a formula?

Whoa, what did I do wrong? Did you see that? Oh no. Hang on a second.

I think I missed it. How many digits are there? If there are eight digits, then I definitely forgot

something. No, no. Okay. There are nine digits, so the last one should be 256. Okay.

256. Okay. So I got it all lined up. At some point I must have not lined it up. My apologies,

but hey, maybe I’m making these mistakes on purpose to make sure that you’re paying attention.

You never know. I want you to think. So 256 is going to be the next number. Double check it with

the calculator. Two to the eighth power, 256. Cool. By the way, a quick trick in binary that

the actual highest number that you can represent in an unsigned binary integer is basically the

strength of the highest digit, you know, this 256 here, multiplied by two and then subtract one

from it. So 256 multiplied by two is going to be 512. So it’s going to be 511. So I could

represent a number between zero and 511 or 512 possible combinations. Okay, so now let’s work

let’s work out the formula.

See 16, 30, 16, 40, okay, I did it okay.

I probably should have rehearsed this.

So let’s do each position.

So it’s either always gonna be one times something

or zero times something, right?

Because binary, these characters can only be one or a zero.

So let’s do on the, starting from the right,

we’ll say one times two to the something power.

It’s gonna be two to the zero power

You know, just going to be a one.

Working our way over to the left, it’s going to be one times two to the something power

to the first power because it just increases every time the power increases.

We have four ones in a row here.

I got to try to remember that.

This is where I’m going to start making lots and lots of typos.

Two to the second power.

And then we have another one.

One, two, three, four, one times two to the third power.

And then again, we are going to hit a zero.

So it’s going to be zero times two to the something power.

You might be tempted to omit the zeros.

You can if you want to.

But for me personally, it helps me quickly visually see that I’m getting the powers in

the right order.

I can see two to the zero power, first power, second power, third power, fourth power.

Sometimes when I omit the zeros, I end up kind of like messing up the order of the powers

and or the order of the exponents.

of the exponents and I have to redo everything all over again.

So I just keep it this way.

Okay, so it’s one, one, one, one, one, one, one, one, zero.

So there’s another zero that we need

times two to the fifth power.

So we got both of those zeros now.

And then we need another one times two to the sixth power.

And then we need

0 times 2 to the 7th power.

Okay.

And then we have another 1 times 2 to the 8th power.

And I know we’re supposed to be done on 8

because that’s what we were doing before.

The 256 strength.

So unless I made some mistakes here,

this is probably the number that we can punch up into the calculator

to see what this binary number is.

So I’m going to punch it up.

Huge.

It says that it’s the number 335.

Let’s see if that’s actually right.

I’m going to punch this up in my personal calculator real fast.

I’m going to say 10101111.

And the expression is decimal 335.

Yep.

So that’s it.

We know how to convert from binary to decimal.

And just again, like as a quick shorthand,

it’s probably a good idea if you’re involved in computer science,

to memorize these positions up to maybe

6, 5, 5, 3, 6.

That might sound a little extreme sometimes,

but I don’t know.

Personally, I’m not like the most advanced

binary reader at all times,

but I can remember up to that much.

And what do I mean when I’m saying that?

I’m saying, you know, start with a 1, 2, 4, 8,

8, 2, 56, 5, 12, 1, 2, 4, 2, 0, 4, 8, 4, 0, 9, 6, 8, 1, 9, 2, 1, 6, 3, 8, 4.

Took me a while to remember that one.

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

So if you think about it, how many bits is this?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.

Right here, 16.

That’ll give you two bytes worth of memorization or a word on many systems.

on many systems. For me personally, I just, I like to go up to 6, 5, 5, 3, 5 because

remember I was saying, you know, what is the highest number that you can go up to

with a certain number of bits? It’s always the power or the strength of the highest bit

multiplied by two and then subtract one. So when I remember 6, 5, 5, 3, 6, that tells me that if I

65535. This is very, very useful if you’re going to be working with binary numbers a lot,

or if you’re taking exams or whatever it is that you’re doing, I would recommend everyone do this.

Okay. What do you say? What do you say we do another binary number, but we’ll just do something

a little bit smaller to make it easy. Okay. So by the way, when you start to memorize these positions,

start to eyeball it, which is really, really fast and a good idea. Like I can see those two

numbers right there. I know the first one is a one and the second one is a two. So that means the

one and the one are just going to be a value of three. Then I just quickly go, all right, one,

two, four, eight, one, two, four, eight, 16. So it’s going to be 16 plus three. So it’s going to

be 19. I guarantee it. Let’s, let’s double check this real fast. We’ll say one times two to the

and then we’ll say 1 times 2 to the first power

and then we’ll say 0 times 2 to the second power

and then we’ll say 0 times 2 to the third power

and then we’ll say 1 times 2 to the fourth power

and if I didn’t go too fast and make a bunch of typos

it should be the number 19

So there is a lot of benefit in memorizing the strength of these different positions.

I personally never remember very much beyond 256 when I’m actually trying to work out a number

conversion, but when I’m just thinking of how to compute things, it’s faster if I can go up to

65536. Okay, I hope you enjoyed this video. I hope you learned a little bit of stuff. I hope

you had a little bit of fun. 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

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somebody subscribed or followed it just wakes me up and I get filled with joy that’s exactly what

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Thank you.

The post Binary to Decimal Made Easy: Fun Crash Course for Beginners appeared first on NeuralLantern.com.

Hey there! Let’s dive into converting decimal to binary—super simple once you get it! I walk you through 55432 and 632, step-by-step, with a few calculator oopsies (I’m not a math whiz either). Learn the divide-by-2 trick, why remainders matter, and how to double-check your work. Plus, a pro tip: don’t just memorize—practice tons! Hit subscribe if you liked it, and let’s keep learning together!

Introduction to Decimal and Binary 00:00:00
Explaining Base 10 and Base 2 00:00:11
Conversion Method Overview 00:01:35
Starting Conversion Example (55432) 00:02:20
Step-by-Step Division Process 00:02:35
Using Modulo Operator 00:02:57
Continuing Division Steps 00:04:04
Reaching Remainder Patterns 00:05:53
Finishing Conversion and Reversing 00:09:17
Double-Checking Binary Result 00:11:51
Second Example Introduction (632) 00:12:52
Conversion Process for 632 00:13:04
Correcting Mistakes in Calculation 00:14:22
Completing 632 Conversion 00:15:56
Learning Tips and Verification 00:16:04
Outro and Subscription Request 00:16:40
Additional Engagement Options 00:17:41

Thanks for watching!

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Hello there.

Let’s talk about converting decimal to binary.

So decimal and binary, if you don’t already know, they’re number representations with

different bases.

So if we have like a decimal, it’s base 10, which means we have the character 0, 1, 2,

to represent a number. We could represent the same exact number in binary as long as you’re

not using like a fraction or anything in binary which is a base 2 because in binary you only have

a 0 and a 1. By the way we can use fractions in binary it’s just that when you start using

fractions then sometimes the numbers don’t translate precisely in every single case.

They often do but not always so. If you’re not using a fraction and you want to convert a number

to binary or binary to decimal it should work you should be able to represent the number exactly

okay so base 10 means we have 10 digits that we can use base 2 means uh two digits or two

sorry two characters or 10 characters and um how do we convert a number okay so the first thing

i’d like to do is let’s see five five four three two is what i wanted to do let’s take a number

And we’ll convert this number into binary.

So the first thing that we do is we try to understand that every single time we have

a temporary number as we’re converting from decimal to binary, we’ll just keep dividing

it by two forever and take the remainder at each step.

The remainder is going to be either zero or one because we divided by two.

When we eventually have nothing left, then we’re done.

and all of the remainders are going to be the binary number so let’s try it I’m

gonna pull up a calculator because I’m not like super sharp at math all the

time I just want to do this quickly remove from favorites was already in

there oh it’s right there the symbol doesn’t make sense the calculate people

have a different symbol and I I’m doing something wrong it’s not showing the

right symbol here I need to fix that okay so 554 32 so the first thing we do

So the first thing we do is we divide it by 2, so I’m going to say 55432, just write down all the steps, it’s a really, really good idea.

55432 divided by 2 is what? It’s something, remainder something.

So the remainder is either going to be 0 or 1, so I’m just going to punch that into the calculator real fast, divided by 2, that’s going to be 27716.

Well, we started with an even number so I can just infer that the remainder is going to be zero.

But if you’re not sure, you can use the modulo operator.

So here when we use the division operator, it’ll tell us what the quotient is.

What’s the actual, you know, what is that number divided by the other number?

But if we use the modulo operator, it’ll just give us the remainder.

Not all calculators do this. Keep that in mind.

7 7 1 6 which was the the result and just multiply it by 2 again if you have the same exact number as you started with

Then you know the remainder is 0 otherwise

You can subtract the original number 5 5 4 3 2 from

The number that you multiplied back up and then that should give you the real remainder. Hopefully your calculator does modulo though

For those of you who are ambitious you can probably just open up a Python terminal and

way because programming languages all have the modular operator and python is pretty easy to get

into all right so we’ve done that we now know that there is a zero somewhere in our binary result

but because we have this result that is pretty big we’re not done we have to continue dividing

so i’m just going to take that number copy paste it to the next line and divide it again

and just repeat the process i’m going to say something divided by two it’s one three eight

check myself here 13858 the original number was even the six was even so I know there’s not going

to be a remainder pretty much you know if it’s even zero remainder if it’s odd one remainder

that’s pretty easy I don’t need to worry about the modulo operator and then I’m going to do it

again copy paste 13858 down to the next line divided by two equals what

2929 so 6929 remainder what?

858 at the end there was even so I’m going to say it’s remainder zero that’s like a lot of zero remainders for me personally

I like to space

My notepad results here out so that everything is lined up notice how the R is kind of like askew

So I’m just going to hit a space there to make sure everything is lined up

And then I’m going to do it again

6929 divided by 2 maybe I’ll hit a space before that

that division symbol to make sure everything is okay.

6929 is going to be, oops, I’m on the wrong.

Did I accidentally close that?

Oh my gosh.

I cannot stop myself.

What?

It’s saying that it was already open somewhere.

Did I just miss that?

No, okay.

Whatever.

Okay.

So 6929 divided by two,

divided by two it’s going to be oh I forgot yeah this calculator is not going

to like around for me so that’s that makes it even easier if the result is

0.5 then the remainder is definitely one otherwise the remainder is zero so it’s

going to be three four six four remainder one three four six four

remainder one space it out real fast three four six four remainder one okay

and then copy three four six four forget about the one we’re not copying that

copying the actual quotient result. So 3464 divided by 2, 1732, 32, remainder 0 because

it was even in the first place, 1732. Oh, there it is. I keep forgetting. Maybe I should

pin this to the top so I don’t lose it. 1732 divided by 2, it’s going to be 866. Whoops,

3 2 divided by 2 equals 8 66 remainder 0 because it was even do my spacing i did my spacing

then we’ll divide again 866 divided by 2 i don’t know maybe my spacing is kind of dumb maybe i

should have spaced the numbers and not spaced the operator that’s probably better okay so 866 divided

433, 433, and it was even, so the remainder is zero.

And then, 433, okay, so 433 divided by two.

I’m getting tired of this.

I don’t know if you can tell.

216, so 433 divided by two is going to be equal to 216,

and then remainder one.

Space that out.

Oh, I messed that up again, okay.

And then space those out, and then everything is good.

those out and then everything is good okay so then 216 divided by two and of

course I’m just doing this again and again and again I hope this is not too

boring but I hope you’re following along another good tip that I like to give

people when they’re learning new things is do not make the mistake of

accidentally memorizing a handful of examples try to find as many examples as

you possibly can and every time you practice use a different example that

way you will actually learn how to do the thing instead of accidentally

accidentally memorizing an example. Okay, so 108 divided by two. Maybe I’ll do this again,

but with a smaller number just to make things faster. It’s going to be 54,

remainder zero, and then 54 divided by two. I guess I can just do this in my head. I don’t

really trust myself, so I’m going to do it over here. Okay, 24 remainder zero, because it was

even and then we’ll do 27 over here that’s definitely going to be a remainder one so that’s

going to be like probably 13 remainder one i don’t trust myself i’m gonna do it for real

27 divided by 2 13 remainder 1 and then put the 13 there 13 divided by 2 is

um 6 remainder 1 oh no i’m losing it okay 6 remainder 1

for double checking. I am honestly not like an internal mind math whiz. And then we do

six divided by two, that’s just going to be three remainder zero. And then we’ll do

three divided by two is going to be, you know, one because only one of the twos can fit there.

And then one remainder one. And then we have one left over. So we’ll say one divided by two,

we can’t actually fit, you know, any twos into the one. So it’s going to be zero.

so it’s going to be zero remainder one and now at this point remember we’re just carrying over

the quotient result we’re not carrying over the remainder so if I carry this over here

zero divided by two the number is always going to just be zero remainder zero no matter how many

times now no matter how many times we carry this down so we know we’re done when this number that

we’re dividing is a zero we’re just totally finished so now I’m just going to omit that

Well, maybe I’ll leave one up there just to kind of prove a point.

Think about this, if this is actually going to be zeros forever, which side of the number

string would the zeros go on so that no matter how many zeros you computed, the actual result

wouldn’t change?

For example, if I had this original decimal number and I decided to say, all right, I’m

going to add some zeros to it without changing the result.

then it definitely changes what number that is, right?

The value is now multiplied by a thousand.

But if I put the zeros on the left,

then the number doesn’t actually change.

These are junk zeros.

They don’t mean anything or they mean nothing.

So that means wherever the endless zeros are

is actually the left side of the binary string

that you’re trying to make.

Think about it.

You know, we’re not going to put a bunch of zeros

on the right side of a binary string

we’d be increasing the size dramatically just based on our whims of how many times we tried

to divide a zero.

Instead if we stick the numbers on the left side, then the result doesn’t change so it’s

totally fine.

Which means if you kind of tilt your head to the left, that’s the number, not to the

right.

So that means you know probably intuitively you might have been thinking oh the first

number, the first remainder we got that was going to be the first digit and then we work

our way to the right.

we work our way to the right no no no actually it’s backwards we have to reverse it so i’m going

to go ahead and um you know you can you can if you want to you know you can start at the bottom

and work your way up and then just write the binary string correctly sometimes i’d like to

start from the top and then reverse the string later just as a little brain exercise so i’ll go

one two three starting from the top one one two three one one two three one one zero one one

And then I’ll reverse it.

I’ll say 1101100010001000.

And because I just did it this way, this provides a nice opportunity to double check your work

because it’s really easy to get things like this wrong.

I get things wrong all the time.

And so if you can figure out a way to double check your work in two or three different ways,

you reduce the chances of being wrong.

It takes a little more time, but it’s a really good idea when you’re actually doing work

or like you’re taking an exam or whatever.

an exam or whatever check your work in multiple different ways so now that I’ve done it in

the first way I’m going to do it from the bottom up just to see if I was right so I’m

going to go one one zero one one zero zero zero one zero zero zero one zero zero zero

does it match it seems to match so I’m pretty confident that this is the correct number let’s

just punch it in real fast I’m going to punch it in on my personal calculator here real

I’m just going to copy this to my outside calculator just to prove to myself that it works.

55432.

Okay, so this is indeed the correct answer.

We now understand how to convert from decimal to binary.

It’s not too bad, right?

Let’s do another number just for fun, just something really small.

Let’s go 632.

Okay, whoops, nope, nope, nope.

Let’s do another tab.

We’ll say decimal 632 so that this is faster.

We start with 632.

We divide it by 2.

632 we divide it by 2 the result is going to be oh can I guess this 350 and then like a 15 and then

a one one I don’t know if that’s going to be right remainder zero let me see if I can punch this up

632 divided by zero I oh I blew it oh I was thinking of okay this is why I use a calculator

316 divided by 2 is going to be, I thought I was so cool too, like, oh, everyone watching

is going to be so impressed that I did this in my mind.

Nope.

So we do 316 divided by 2, it’s going to be 158 remainder 0.

So 158 divided by 2, that’s going to be, okay, that’s 75 plus 4, I guarantee it.

So I’m going to do 79, 79 remainder 0.

Let me see if I’m right.

Oh gosh, this is going to be embarrassing if I get it wrong.

79, okay.

So then, now we’re gonna do 79 divided by two.

Whoops, I spaced poorly.

79 divided by two is basically gonna be 39 remainder one.

We know it’s remainder one,

cause you know, 79 is odd.

If it was 80 divided by two, it would’ve been 40.

So let’s just double check real fast

to make sure that we’re getting it right.

It’s easy to get things wrong

if you’re not double checking yourself.

39, okay, so then we’ll do 39 divided by two.

divided by 2

well that’s just going to be 20 remainder 1

am I right about that? I don’t know

let’s see

39 divided by 2

oh I blew it

what was I thinking?

of course it’s going to be at least 40 if it’s 20

totally blew it

so 19 divided by 2

ok so I’m looking for a lower number not a higher number

so 18 so that’s 9

let me see 9 remainder 1

am I right?

Am I right? By the way all these shenanigans that I’m doing right now are exactly how I’m gonna end up with the wrong result

And have to do this whole thing all over again from scratch, but hey at least it will be more brain exercise

Okay, so 9 divided by 2

I’m gonna say 4 remainder 1 because it’s odd

We’ll do 9 divided by 2 just to double check and then we’ll say 4 divided by 2 is

think I need to double check it although I probably should anyway 2 divided by 2 is going to be 1

remainder 0 okay we have a 1 so we actually have to do this one more step 1 divided by 2 equals

1 remainder 0 oh sorry sorry sorry sorry 0 remainder 0 otherwise that would have been

infinity 1s for no reason at all so 0 remainder 0 sorry remainder 1

Then finally, we’re down to 0 divided by 2 equals just 0, remainder 0.

And then we’re finished.

Okay.

Let me do it the first way where I go from top to bottom, then reverse it.

1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 1, 2, 3, 4.

Then I’ll try to reverse that.

1, 2, 3, 4, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3.

Okay.

Then I’ll do it from the bottom up.

1, 2, 3, 4, 1, 0, 0, 1, 2, 3, 4, 1, 2, 3.

two, three, do these two match?

Yes, they do.

Okay, I think we’ve successfully done this.

We’re now semi-experts at converting decimal to binary.

Thank you for watching.

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.

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?

It’s a 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 do me a kindness and and subscribe

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 of

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

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if you have a suggestion for clarifications or errata or just future videos that you want to

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just send me a comment whatever I also wake up for those in the middle of the night I get

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 coming for us all

Thank you.

The post Decimal to Binary Made Easy (Even I Can Do It!) appeared first on NeuralLantern.com.

Hello there! Ever wondered what number bases are all about? In this video, we?re diving into decimal (base 10 – the one you already know), binary (base 2 – just 1s and 0s, how your computer thinks), and hexadecimal (base 16 – the compact cool kid). I?ll show you how the same number looks totally different across these systems – binary gets LONG, hex keeps it short and sweet. Plus, why do we even use hex? Spoiler: it?s a game-changer for reading computer memory. Stick around to learn handy prefixes like 0x and 0b to avoid mix-ups. Want to be as cool as those binary-converting pros? Hit subscribe, scan the QR code for more, and let?s geek out together in the next video – conversions are coming up! Drop a comment with your thoughts or just say hi – it might wake me up in the middle of the night with joy!

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Hello there. Let’s talk about number bases. So what are number bases? You’ve probably at some

point heard someone say, hey, I can convert between decimal and binary or between decimal

and hexadecimal or hexadecimal and binary. And you thought that that person was way cooler than you

were. Well, they are way cooler than you. But if you watch my videos, maybe you can be just as cool

Anyway, so what do we mean by number basis exactly?

We’ll start with decimal,

which is the number system that everybody already understands, I hope.

So in decimal, you have 10 characters, right?

So we’ll say like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

It’s like 9, or sorry, 10 possible characters.

So decimal is actually base 10.

I’m going to write base 10 here.

Decimal is base 10.

base 10 because it has 10 available characters. The next thing is binary. You’ve probably heard

of that before. Even a lot of non-computer scientists understand binary at least a little

bit because it’s just ones and zeros, right? This is how your computer represents information.

All characters, all numbers, all floats, all everything. They really just come down to zeros

and ones inside of the computer. And it’s not like there’s an actual zero or an actual one anywhere.

It’s more like there’s a certain voltage that represents a one or there’s a different voltage

represents a 1 or there’s a different voltage that represents a 0.

You can think of it as just like voltage or no voltage, but that’s not always the case.

But you know, long story short, it’s just 1s and 0s.

So in binary, we can just represent a 0 or we can represent a 1 and that’s it.

Because there’s only two characters that we can use to represent numbers, we call this

base 2.

So that’s binary.

Now not a lot of people have heard of hexadecimal outside of computer science, but hexadecimal

outside of computer science but hexadecimal is a number is another

number system that we can use which uses base 16 the reason we use hexadecimal is

it because it kind of it kind of compacts a number I’ll show you in a

second how it can represent the same number but with less characters you can

imagine in binary if we have base 2 there’s only two characters that means

the same number in decimal versus binary it’s probably going to be a lot longer

imagine that, right?

Because it’s not like the actual numbers change

that we’re trying to represent.

It’s just that the representation changes.

So hex or hexadecimal,

we have 16 different characters.

Did I say 15 a moment ago?

Sorry if I did.

So we start with the normal ones that base 10 has,

decimal has.

So we go three, four, five, six, seven, eight, nine.

So that’s 10.

the extra five, we do A, B, C, D, E, F. Sorry, extra six. I knew I was going to say five at some

point. So in hexadecimal, we have the characters zero, one, two, three, four, five, six, seven,

eight, nine, and then A, B, C, D, E, F. For a total of 16 characters, or one digit can represent

here. So this is the basics of the differences between the number systems. Let me show you a

quick example. Let me see if I got my calculator here. Hopefully it’ll work. Okay. I’m going to do,

let’s see, variables. So how do you get into this one? Mode. Oh, number base. So I’m going to do,

let’s just pick a random number in decimal. So I’m going to say like, you know, just hit the

So you can see that if I type a number in decimal and show it in decimal, then well,

it’s the exact same size as you probably have suspected.

But if I represent this exact same number in binary, you should probably expect that

the representation is going to be way longer because again, binary only has two characters

to work with.

So it’s harder for it to represent the same information.

So I’m going to change the expression base here to binary.

Oh no, what’s happening?

What’s going on here?

Expression base.

Oh, I did the wrong thing.

Decimal is the expression base.

Binary is the result base.

Okay.

So that same number that we had before, 871, 876, 42,

look at how huge it is in binary.

Takes up a lot of your screen, right?

So we use binary because it’s the closest representation

to what the actual machine has.

So that’s good.

Especially if you want to start manipulating individual bits

manipulating individual bits for one reason or another. It’s good to know how to, it’s good to

understand binary. But hexadecimal is useful, like I said before, to compact the same number. So

again, because the base of the original number is 10, you know, we had the original number in decimal.

If we show a hexadecimal version of it, it should be shorter because there’s 16 characters to work

with. It’s easier for it to represent the same information. So the result base, I’m just going

hexadecimal here and look at how short that number is the original number is one two three four five

six seven eight it’s eight characters long but the hexadecimal number is two four six seven

characters long and that savings in characters will go up and up and up the more you know the

longer the original or the bigger the original number is let me see if I can just add some more

numbers here okay let’s see if we get more savings here one two three four five six seven eight nine

Okay, so the original number is 15 long and here we have 2, 4, 6, 8, 10, 12, 13.

So that’s a savings.

Now think about it this way.

This is a huge savings compared to binary.

Let’s go back to binary real fast.

Same number, which is currently in hex.

As soon as I start showing it in binary, the number explodes.

So there are a lot of numbers, especially if you have a 64-bit number, which you work

if you were to just take you know one of those 64-bit numbers and try to express it in binary

it’s just kind of like it’s really really long and if you want to represent anything even a little

bit bigger like 128-bit numbers or even the contents of memory from you know one memory

location to another binaries just can explode and fly off the screen so this is why I mean this is

one of the biggest reasons why we use hexadecimal because it’s just it’s easier to see what’s inside

of the computer it’s easier than decimal and it’s easier than binary at least once you understand

hexadecimal one other thing that i want to uh show you real fast let me see like let me change

that back to decimal so i don’t screw myself later okay um suppose that you wanted to represent a

number in binary sorry let’s say decimal well you know we’ll say like one two three four right and

well actually let’s not do one two three four let’s say like a thousand and one and then you

want to represent a number in binary and you write one zero zero one and then you want to

represent a number in hexadecimal you could also have one zero zero one right the problem is that

each of these numbers are actually different numbers they only look the same because the

character representation is the same but not the actual number so how do you uh how do you sort of

How do you sort of like differentiate and make sure that the person reading the numbers that you’ve written down knows what base they’re in?

Because if you know if you’re a computer scientist or you’re doing some kind of crazy math, then

well, it might not be obvious and

you want to be careful that the person doesn’t misinterpret your results.

Okay, so let me do that thing again real fast

just to prove to you. What am I doing here? Units? No.

Mode.

Okay, so I’m going to say if I write 1001, I’m going to display it as decimal,

but the input is first going to be decimal.

So in decimal, 1001 is 1001.

Okay, that’s fine.

But if this 1001 was actually a binary number,

I’m going to say that the expression base is binary here.

Notice how the real number is actually 9 if you represented it in decimal.

expression like the original number was you know the characters were hexadecimal then the real

decimal version of 1001 would be 4097 that’s three totally different numbers so you got to be careful

that you know what you’re reading and you got to be careful that you help the person reading what

you’re writing down if you’re trying to transmit this information so with hexadecimal a really

really common prefix that everyone should use is ox ox and then any number after that usually just

reading this is a hexadecimal number so there’s no ambiguity same thing for binary you’ll just say

like ob and then for decimal you just just leave it alone i think there’s a another prefix you can

use but i usually don’t use anything but at least uh ob says this is binary and ox means this is

hexadecimal and then nothing just means okay just default to human reading just decimal

okay this was the basics of number bases in other videos i’m going to talk about how to actually

between these three bases maybe in the future at some other point in some other

video far off in YouTube land I might talk about octal or some other base but

in the immediate future it’s going to be decimal binary and hexadecimal so I

hope you’ve enjoyed this video I’ll see you in the next

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

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 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

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 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 this video and it’ll take you to my

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 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 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 Master Number Bases: Decimal, Binary, and Hexadecimal Explained! appeared first on NeuralLantern.com.