Struggling with converting decimal fractions to binary? In this fun, beginner-friendly tutorial, we dive into how to convert numbers like 45.8046875 to binary and back to decimal, step by step! Learn the multiplying-by-2 method, handle precision loss, and understand fractional binary representation. With real examples (0.126753, 0.84375), you’ll master this key computer science skill. Perfect for students, coders, or anyone curious about how computers store numbers. Subscribe for more tech tutorials, and let me know what you want to learn next! Visit [YourWebsiteLink] for more. #Binary #DecimalToBinary #ComputerScience #TechTutorials

Introduction to Decimal-Binary Conversion 00:00:00
Understanding Fractional Binary Numbers 00:00:15
Fractional Binary Representation Basics 00:01:00
Converting Decimal Fractions to Binary 00:04:06
Example: Converting 0.126753 to Binary 00:04:52
Precision Loss in Conversions 00:05:36
Example: Converting 0.84375 to Binary 00:09:57
Converting Binary Fractions to Decimal 00:14:22
Example: Converting Complex Number 45.8046875 00:16:48
Combining Whole and Fractional Parts 00:21:00
Conclusion and Verification 00:23:25
Outro and Community Engagement 00:24:16

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Hello there, let’s talk about how to convert decimal numbers with fractions into binary

numbers with fractions and vice versa.

So up to this point, if you’ve been watching my other videos, you probably know that you

can easily convert a decimal number to binary and binary to decimal if the decimal and binary

numbers but in order to progress towards IEEE 754 representation in other words

in order to eventually be able to represent binary numbers with fractions

like floats or doubles in the machine you have to start learning how to get

the fraction part of a decimal number into binary the way we’re going to do

it in this video it’s not actually going to be the final representation of how

your machine stores floating point numbers but it’s an important step on

on the way there. Without this step, you probably wouldn’t be able to do it.

So what am I talking about? I’m just going to open up this notepad real fast and just show you

that what I really mean is, suppose we have like a number 45 point blah, blah, blah, blah, blah,

right? So this is the whole part and this is the fractional part. Okay, no problem. Also in binary,

we have like a bunch of ones and zeros. This is a whole number, but we could put a decimal point

and then just start doing more numbers after the decimal point in order to represent a

in order to represent a fractional binary number.

Okay, so let’s see.

We know, hopefully at this point, if you watch my other videos,

that, I don’t know, I’m just going to put some random numbers here

and then like some more random numbers there.

And you know that the strength of each of these numbers

is sort of like increasing by powers of two on the left side, on the whole side.

So the strength of that first digit is one.

digit is one the next digit has a strength of two and then four and then eight and then 16 maybe i’ll

put the six up here and then 32 so three and two and then 64 and maybe i’ll do another digit i’ll

just put like a zero there and then you know the left most digit has a strength of 128 so basically

a 1 or a 0 for the actual binary number multiplied by its strength. So 1 times 1 is 1, add that to

0 times 2, add that to 1 times 4, and 0 times 8, and 1 times 16, and so forth, right? So hopefully

we know how to do that at this point. To do the same thing on the fractional side, maybe I won’t

put a decimal marker there, it’s really the same deal except as we go left, we were multiplying by

have more power more strength but as we go to the right past the decimal point they should have less

strength and we’ll just divide them by two so pretty much at this point let’s see we’ll have

one half will be the strength of this digit right here whoops one half so the strength that that

digit has is just one half the strength that the next digit has is going to be one fourth remember

1 4th remember you multiply sorry you divide by 2 each time whoops I’m getting lost oh man I

probably need to add some spaces because it’s starting to get pretty ugly so this digit has

a strength of 1 half this digit has a strength of 1 4th and then we’ll just say that the next one

has a strength of 1 8th and so forth we’ll just keep dividing by 2 each time so don’t forget that

don’t make the mistake of saying 1 4th or sorry don’t make the mistake of saying 1 half 1 3rd

one half, one third, one fourth.

Don’t increase the denominator by one.

You want to multiply, or sorry,

you want to divide by two each time.

Or if you want to say the word multiplication,

then you multiply by 0.5, I guess, if you want to.

I’m just going to write 1 16th

and then just be done with the divisions.

I hope you understand what I’m talking about.

We’re going to do some examples right now.

Okay, so let’s calculate.

Well, actually, let’s just, just to emphasize, just to make sure everybody understands, what

we would do to convert such a number from binary to decimal would basically be, you

know, compute the left side as if it were a whole number.

I’m going to put W for whole number.

And then separately convert the fractional part as if it were just, you know, zero point

something.

And then just combine the two things when you’re in decimal.

And you’ll do the same thing when converting a number from decimal to binary.

decimal to binary you convert the whole part first put that into ones and zeros then convert the fact

the fractional part into a fractional binary part and then just combine them across the decimal point

so let’s do an example let’s start with converting 0.126753 i don’t think that this number is going

to resolve easily it’s kind of like a good lesson here when you’re converting between binary and

there are always going to be some numbers in in in decimal that you can’t represent in binary

and vice versa there are always going to be some numbers in binary that you can’t represent in

decimal so it’s not that decimal or binary or you know superior or inferior i mean all technology

is pretty much running on binary so it can’t be that bad but um just keep that in mind some numbers

that you type randomly are just never going to resolve and you’ll have to give up at some point

have to give up at some point and say, well, we’re just going to call this a precision loss

because we just, we just have to like give up, especially if you only have so many bits

to put the fraction in. Okay. So what am I going to do? What’s the, what’s the basic algorithm

here? There are lots of different ways to do it. The way that I’m going to show you is just

multiplying by two. So if we take, you know, 0.126753 and we multiply it by two,

We end up with, let’s see, times 2.

Whoops, hello.

Oh, I got to do that.

Times 2.

We’re going to end up with a different number.

If the number is equal to or greater than 1,

then we will say that we have achieved a number of 1 for the converted binary number.

And if not, we’ll say we have achieved a number of 0.

If the number is 1, we’ll also subtract 1 from the remaining number here in decimal.

The result we have is just, what’s going on?

Oh, I somehow turned on my annotator.

Okay.

In this case, we just have, you know, this number right here.

It’s not greater than one or equal to one.

So I’m just going to say this gave us a binary number of zero.

And because it gave us a zero, we’re not actually going to change it at all.

We’re not going to subtract one from it.

We’re just going to leave it as is.

We will then multiply by two again.

by 2 again. So I’m just going to say, do it one more time. We’ll say this multiplied by 2,

and it’s going to be this number. Again, it did not exceed or equal 1, so the bit in that position

is going to be a 0, and we’ll just copy and carry it over just as is. Do it again, and we’ll say

Now we have a number that equals or exceeds one.

So we’ve achieved a one in the binary position.

So it’s going to be a one here.

Then we got to subtract one.

So we’re just going to be left with 0.014, 024 and whatever.

And then we just continue.

Maybe I’ll do it a couple more times,

but I’m going to give up because I don’t think

that this number will translate completely.

So I’m going to say multiply by two again,

and it’s going to give us,

hang on a second here.

What was that?

Hang on a second here. What was that? That was one. Oh, I forgot to subtract one. So I got to

subtract one. And then I’m going to multiply by two. Now we get this number right there.

This is not equal to or greater than one. So the bit is going to be zero.

And then that means the remaining number is just going to be the same thing.

We’ll do another. Actually, let me let me clean the calculator for a second here.

going to select this whole thing and just paste that and I’m going to say

multiplied by two that’s going to be that new number and I think you’re

starting to understand why I want to give up because we’ll just be kind of

doing this forever this might end up being an irrational number in binary I

don’t really know I haven’t gone that far but it’s definitely gonna take a long

time so I’m gonna give up and I’m just gonna say all right the final binary

number is gonna be 0.00100 and then just say maybe there’s some more stuff at

maybe there’s some more stuff at the end we’ll just call this a precision loss

you can see well maybe I should do one more number actually because it it’s kind of a mirror there’s

like two zeros and then a one and then two zeros on the other side let me multiply this by two

real fast just to show you without symmetry what would happen so I’m gonna multiply that by two

and it’s gonna be this number right here so that’s gonna be zero because it didn’t exceed

or meet one and so the number we have left over is just that okay so now

because there’s no symmetry you can see that the number is going to be point

zero zero one zero zero zero we go from top to bottom we don’t do any kind of

reversal like you might do with whole number binary conversion I don’t know

maybe it’ll be zero for a long long long long time and never or yeah they’ll

probably be some ones in there at least I don’t know if it’s ever going to

resolve you’ll know you’re finished when the

Here is a zero.

So again, I’m just going to give up on this because I don’t really know if it’s going to work.

Let’s do a number that I know is going to resolve.

I have this one prepared in advance.

So let’s do 0.84375.

Okay.

So how do we convert this?

Again, just multiply by two.

Every single time you meet or exceed one, then you’ll say that we have a one in the binary number.

binary number and then subtract one after that and if not we will say that

we have a zero in the binary position and then we won’t subtract one okay so

that number multiplied by two is going to be point one six eight seven five so

that’s definitely greater than or equal to one so I’m going to say we have a one

in the binary position and then the next number is going to be just be zero point

now we take that number 6875 you could also just you know in your calculator you could say minus

one and then we’ll multiply it by two to get the next bit the number is going to be 1.375 so i’m

going to write 1.375 here and then it’s greater than or equal to one so it’s going to be another

one here and then after we subtract one it’s going to be 375 no problem okay so let me just

And then multiply by 2 to get to the next bit position.

It’s going to be 0.75.

All right, so 0.75, that number is less than 1, so we have a 0 in that bit position.

We also don’t subtract anything because we had a 0 in that bit position.

Then we just multiply by 2 again.

Multiply by 2, now we have 1.5 because that’s greater than or equal to 1.

We have a 1 in that bit’s position, then we subtract 1.

one it’s just going to be 0.5 that should be pretty easy right because that’s that sounds

like there’s a one in a bit and then it’s just done after that so i’m going to do minus one

and then multiply by two again notice how that is exactly a one so it’s going to be 1.0

which means we have a one in the position because it is equal to or greater than one

and then uh well what we have left over is zero

Zero multiplied by two is going to be zero.

So that means if we kept doing this forever,

then all the numbers down here are just going to be zeros forever.

And I said in another video,

when you realize what’s going on with the zeros,

like where are they?

Are they on the left or the right?

When you’re converting a whole number from binary to decimal or decimal to binary,

the zeros would be on the left side.

So that’s why we would reverse

because if you just add infinity zeros on the left of a whole number,

you’re not changing the value.

number you’re not changing the value but if you added them to the right you’d be increasing the

value when it comes to the fractions the right side of the fraction won’t change the number for

example if we had you know one point and then some like random binary numbers if we just kept adding

zeros on the right side that’s not changing the value of the number because this is the fractional

part however if we started adding numbers on the left side then we would make the fractional part

smaller and smaller and smaller so that means the zeros have to be on the right side and you can see

and you can see here the right side is the bottom so that means we’re going to take these numbers

I’ll just put etc here just so you can see etc that means we’re going from top to bottom so the

final number is 0.11011 and then a bunch of zeros after that are just you know nothing

and that’s the final answer we now have 0.84375 is equal to binary that number and we’ll just say

that number and we’ll just say OB to to indicate that the following is a binary

number because again you could have a decimal number and then have like a

bunch of like ones and zeros in the fraction part I guess so to make sure

that the reader understands what they’re seeing you’ll say OB to indicate this is

a binary number on exams or quizzes if you’re out there doing this for an exam

or a quiz keep in mind you probably want to talk to professor to make sure that

ob is supposed to be part of your answer they might just want this it depends anyway so 0.11011

okay then let’s convert it back again let’s let’s convert this number to the original decimal number

there okay so how can we do that pretty much just start adding the fractions up so remember the

Remember, the first fraction that we see is going to be one half.

One half.

And the second fraction we see is going to be one fourth.

And then we just keep multiplying.

One fourth, one half.

Maybe I should write this in a notepad here.

We’ll see one half plus one fourth plus one eighth.

And some of these bits aren’t going to count.

Like, for instance, the one eighth, it’s not going to count towards the fraction.

But for me personally, if I forget to type one eighth,

I’m probably going to accidentally use it for the next position.

So I’m just going to type everything one at a time.

So let’s see, we have one, two, three, four, five, one, two, three, four.

So I got to do one more plus one 32nd and then multiply by the bits.

So say like, you know, one times that and then one times that and then zero times that

to basically, you know, cancel it out.

And then one times that and then one times that.

plug it all into the calculator

let’s see if I got that right

0.84375

so that’s how you convert

back from binary to decimal

pretty easy and then also

of course when you’re practicing this you want to try

with a bunch of different random numbers to start off with

you just want to be

careful again this process

could take forever if you have like

you know the wrong number that you

start with but I guess at least

at least when we’re converting from binary to decimal it’s going to end up resolving to something

uh it won’t necessarily be something that you can’t represent but you know if you start

up with a random number in decimal there’s a chance maybe it’s not going to work with binary

okay well you have to give up and call it a precision loss okay so then now let’s uh let’s

ask what if we had a complex number because we know how to do this now with just the fractional

now with just the fractional part but what if we had a number that was um a little bit more

difficult let’s say we have wait a minute you know for you know for 37 5.

oh i think i just accidentally did a totally different number than i wanted to on my plan

luckily i got the right answer okay

Anyway, what if we had a more complicated number?

Let’s see, 804, 6875.

Okay, so 804, 6875, but with a 45 in front of that.

Remember we said before that this is the whole part

and this is the fractional part,

and you just wanna do them separately

and then combine them afterwards.

So the whole part, let’s see, what is that gonna be?

I’m just gonna say that this is not a video

for whole number binary conversion.

This is just dealing with fractions.

just dealing with fractions. Find my other videos if you want to know how to convert the whole part,

but I’m going to say that 45 is just this number in binary. And you can double check real fast.

You can say 1 plus, here let’s do it again, let’s do it just to be sure. 1 plus not a 2 because

there’s a 0 there, and then we’ll say 4 plus 8 plus not a 16 because there’s a 0 there, and then

plus 32. Add that together, that’s 45. So the whole number part is pretty easy if you already know how

number part is pretty easy if you already know how binary conversion but now let’s convert point uh

zero eight zero point eight zero four whoops screenshot no thank you zero point eight oh four

six eight seven five so i’m gonna have to do this from scratch since this is a different number than

i just worked with we’ll do that multiplied by two and it’s going to be this number

is that really not the same number?

Yeah, I guess I really just did a different number.

Okay, so that means we’re going to have a 1 in the binary position

and the remaining fractional part is just going to be this.

Whoops, zero point that.

So then we take that number and bring it down.

Multiply it by 2.

Whoops, not supposed to actually bring that part down.

We’ll bring it into the calculator.

We’ll multiply it by 2.

actually let me get that again and subtract one just to double check myself it’s always good to

double check yourself then we’ll multiply this by two and then the number is going to be point

1.28 so we have that and then since it’s either equal to or greater than one it’s going to be

you know a one in the binary position so 0.21875 is going to be the remainder there

so I’m going to do minus 1 and then times 2 to make sure the calculator agrees with me whoops

21875 okay then I’ll do a multiply by 2 to get the next number 4 3 7 5

and that’s not equal to or greater than 1 so we’ll put a 0 there and we won’t subtract anything

so it’s just going to be 0.4375 again then we’ll multiply that by 2 to get the next number

times two it’s going to be 0.875 so 0.875 again this is not one or greater so we have zero in

the binary position and we don’t subtract anything 0.875 multiply by two again times two so it’s

going to be 1.75 1.75 and then of course we’ll have a one in the binary position and the leftover

0.75 so let me just go back to the calculator and I’ll say minus 1 times 2 it’ll give us 1.5

so 1.5 over here means we’ll have a 1 in the binary position because it was equal to or greater

than 1 the leftover is going to be 0.5 now you know we’re about to finish because 0.5 times 2

is just going to be 1.0 which will give us a 1 for the binary part and then the remainder is going

remainder is going to be 0.0 and then you know there’s no need to multiply 0 by 2 because it is

forever going to just be zeros uh maybe i’ll just write it out one more time just so you know 000

right remember that so that means of course the zeros are on the right side of the fractional

part and on the left side is going to be 0.110011

1100111 and then now we just have to combine those two numbers so maybe just I’ll put something

here indicating that this is the conversion of just that number like that now we’ll combine

both of those parts right so 45 was this so I’ll say maybe therefore this big number right here

combine this number for 45 and then I’ll just put a decimal point and then I’ll put the fractional

part on the right side and then let me just double check my work real fast it should be

10110111 wait wait what no no 101101 and then 1100111 okay so that’s it we’ve converted

converted a complicated decimal number into binary.

And we can do it in the reverse, just using the same thing.

You know, step one, convert this number into a whole number of decimal.

And then step two, convert this number into a whole number,

sorry, a just only fractional number for decimal

by just getting the one half plus one fourth and so forth.

put them around a decimal point just for practice okay I’ll go ahead and do it

some of you are probably like why won’t you do it I’ll do it okay so just only

looking at the fractional part because that this is not a video to convert

whole numbers in binary and decimal but just to convert the fractional part only

I’m gonna do let’s see say whoops whoops whoops whoops whoops whoops maybe I need

Okay, so starting with just this one right here,

it’s going to be 1 half plus 1 fourth plus not 1 eighth, not 1 16th, a 32.

1 32 plus 1 over 64 plus 1 over 128.

0.8046875.

So it looks like we succeeded.

Okay, so now we know how to convert

a decimal number with a fraction

into a binary number with a fraction.

And we also know how to convert

a binary number with a fraction

to a decimal number with a fraction.

That feels like a long video.

Let’s see what it is after I cut this.

Thank you so much for watching.

I hope you learned a little bit of stuff

and you had a little bit of fun.

I will see you in the next video.

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The post How to Convert Decimal Fractions to Binary (and Back!) – Easy Step-by-Step Guide appeared first on NeuralLantern.com.

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!

Find us on other social media here:

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Please help support us!

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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

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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

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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?

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So please do do me a kindness and and subscribe

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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

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

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.