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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

the sign.

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

mean negative or what means what?

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

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

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

That’s positive.

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

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

then we definitely know that this number is now negative.

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

because the numbers don’t work out the same anymore

in two’s complement.

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

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

but they’ll still be valid in order,

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

subtract them from each other and things like that.

So two’s complement is pretty cool.

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

Oh, one thing to understand is that

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

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

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

total combinations.

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

and all the rest will be value bits.

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

In this case, the range kind of goes down.

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

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

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

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

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

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

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

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

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

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

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

255 possible combinations with seven bits.

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

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

Anyway. Okay.

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

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

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

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

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

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

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

easy.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Let’s start off with the number negative 109.

Okay, how do we do this?

The first thing is convert it to its positive form.

Take the absolute value. Okay.

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

and that’s just going to be positive 109.

Okay, no problem.

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

Now we’ll convert it to binary.

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

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

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

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

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

actual number.

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

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

Mmm, maybe like

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

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

Then it’s going to be minus 40

So it goes from 45 to 13.

So then that was the 32.

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

Is 16 less than 13?

No, it’s not.

So we’ll put a zero here.

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

Four is definitely less.

So I’ll put a one bit there.

And then I’ll subtract four.

And then one, two, four.

Oh, wait a minute.

One, two, four, eight.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

But sometimes that might not be the case

because what if we already had a one there

and we had to add one to that?

Well, we’d add one to the right side

and it would turn into a zero

and then it would carry a bit to the left.

That would become a zero

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

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

when you add two binary numbers together,

you have to be careful.

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

For each digit’s position,

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

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

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

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

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

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

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

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

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

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

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

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

Okay, so how do we add these?

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

Zero plus one is one, no carry bit.

One plus zero is one, no carry bit.

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

One plus zero is one, no carry bit.

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

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

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

So we’ll just do that for now.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

then just, you know, keep that in mind.

Okay, so 128 is not smaller than 29.

64 is not.

32 is not.

16 is, though.

So I’ll put a 16 bit there.

And I’ll just subtract 16 from 29.

29 minus 16.

Now we’ve got 13 left.

So 64, 32, 16.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

or something like that.

Next, convert to binary.

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

Oh my gosh.

Next, flip the bits,

which is gonna be 1110010.

Okay.

So now we take this bit flipped number

and we will add one.

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

one, oh, it’s too easy.

Maybe I got excited and I thought,

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

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

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

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

Let me start from the right side.

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

Let me just double check here.

One one one zero zero zero.

OK, so I got that.

Now we have.

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

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

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

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

unless you’re like really, really practiced.

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

indicating that it’s a negative number.

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

using 2’s complement.

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

let’s say, 29 from 109.

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

109 minus 29.

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

Let’s see, convert to binary.

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

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

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

let me make sure that I grab the right one.

Invert the bits, okay.

So positive 29 is this number.

Whoops.

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

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

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

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

i’ll say aka

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

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

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

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

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

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

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

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

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

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

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

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

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

drag this down

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

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

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

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

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

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

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

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

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

Now we have a three.

Oh, that’s kind of nice.

So this is an interesting edge case kind of.

One plus one plus one is three.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

109 minus 29 whoops what happened here 109 minus

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

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

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

As you can tell from this video alone

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

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

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

So let’s see

Hmm

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

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

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

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

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

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

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

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

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

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

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

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.

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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The post Binary to Hex Conversion Made EASY! No Math Needed! 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.

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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.

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