Hey there! Let’s dive into converting decimal to binary—super simple once you get it! I walk you through 55432 and 632, step-by-step, with a few calculator oopsies (I’m not a math whiz either). Learn the divide-by-2 trick, why remainders matter, and how to double-check your work. Plus, a pro tip: don’t just memorize—practice tons! Hit subscribe if you liked it, and let’s keep learning together!
Introduction to Decimal and Binary 00:00:00
Explaining Base 10 and Base 2 00:00:11
Conversion Method Overview 00:01:35
Starting Conversion Example (55432) 00:02:20
Step-by-Step Division Process 00:02:35
Using Modulo Operator 00:02:57
Continuing Division Steps 00:04:04
Reaching Remainder Patterns 00:05:53
Finishing Conversion and Reversing 00:09:17
Double-Checking Binary Result 00:11:51
Second Example Introduction (632) 00:12:52
Conversion Process for 632 00:13:04
Correcting Mistakes in Calculation 00:14:22
Completing 632 Conversion 00:15:56
Learning Tips and Verification 00:16:04
Outro and Subscription Request 00:16:40
Additional Engagement Options 00:17:41
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Hello there.
Let’s talk about converting decimal to binary.
So decimal and binary, if you don’t already know, they’re number representations with
different bases.
So if we have like a decimal, it’s base 10, which means we have the character 0, 1, 2,
to represent a number. We could represent the same exact number in binary as long as you’re
not using like a fraction or anything in binary which is a base 2 because in binary you only have
a 0 and a 1. By the way we can use fractions in binary it’s just that when you start using
fractions then sometimes the numbers don’t translate precisely in every single case.
They often do but not always so. If you’re not using a fraction and you want to convert a number
to binary or binary to decimal it should work you should be able to represent the number exactly
okay so base 10 means we have 10 digits that we can use base 2 means uh two digits or two
sorry two characters or 10 characters and um how do we convert a number okay so the first thing
i’d like to do is let’s see five five four three two is what i wanted to do let’s take a number
And we’ll convert this number into binary.
So the first thing that we do is we try to understand that every single time we have
a temporary number as we’re converting from decimal to binary, we’ll just keep dividing
it by two forever and take the remainder at each step.
The remainder is going to be either zero or one because we divided by two.
When we eventually have nothing left, then we’re done.
and all of the remainders are going to be the binary number so let’s try it I’m
gonna pull up a calculator because I’m not like super sharp at math all the
time I just want to do this quickly remove from favorites was already in
there oh it’s right there the symbol doesn’t make sense the calculate people
have a different symbol and I I’m doing something wrong it’s not showing the
right symbol here I need to fix that okay so 554 32 so the first thing we do
So the first thing we do is we divide it by 2, so I’m going to say 55432, just write down all the steps, it’s a really, really good idea.
55432 divided by 2 is what? It’s something, remainder something.
So the remainder is either going to be 0 or 1, so I’m just going to punch that into the calculator real fast, divided by 2, that’s going to be 27716.
Well, we started with an even number so I can just infer that the remainder is going to be zero.
But if you’re not sure, you can use the modulo operator.
So here when we use the division operator, it’ll tell us what the quotient is.
What’s the actual, you know, what is that number divided by the other number?
But if we use the modulo operator, it’ll just give us the remainder.
Not all calculators do this. Keep that in mind.
7 7 1 6 which was the the result and just multiply it by 2 again if you have the same exact number as you started with
Then you know the remainder is 0 otherwise
You can subtract the original number 5 5 4 3 2 from
The number that you multiplied back up and then that should give you the real remainder. Hopefully your calculator does modulo though
For those of you who are ambitious you can probably just open up a Python terminal and
way because programming languages all have the modular operator and python is pretty easy to get
into all right so we’ve done that we now know that there is a zero somewhere in our binary result
but because we have this result that is pretty big we’re not done we have to continue dividing
so i’m just going to take that number copy paste it to the next line and divide it again
and just repeat the process i’m going to say something divided by two it’s one three eight
check myself here 13858 the original number was even the six was even so I know there’s not going
to be a remainder pretty much you know if it’s even zero remainder if it’s odd one remainder
that’s pretty easy I don’t need to worry about the modulo operator and then I’m going to do it
again copy paste 13858 down to the next line divided by two equals what
2929 so 6929 remainder what?
858 at the end there was even so I’m going to say it’s remainder zero that’s like a lot of zero remainders for me personally
I like to space
My notepad results here out so that everything is lined up notice how the R is kind of like askew
So I’m just going to hit a space there to make sure everything is lined up
And then I’m going to do it again
6929 divided by 2 maybe I’ll hit a space before that
that division symbol to make sure everything is okay.
6929 is going to be, oops, I’m on the wrong.
Did I accidentally close that?
Oh my gosh.
I cannot stop myself.
What?
It’s saying that it was already open somewhere.
Did I just miss that?
No, okay.
Whatever.
Okay.
So 6929 divided by two,
divided by two it’s going to be oh I forgot yeah this calculator is not going
to like around for me so that’s that makes it even easier if the result is
0.5 then the remainder is definitely one otherwise the remainder is zero so it’s
going to be three four six four remainder one three four six four
remainder one space it out real fast three four six four remainder one okay
and then copy three four six four forget about the one we’re not copying that
copying the actual quotient result. So 3464 divided by 2, 1732, 32, remainder 0 because
it was even in the first place, 1732. Oh, there it is. I keep forgetting. Maybe I should
pin this to the top so I don’t lose it. 1732 divided by 2, it’s going to be 866. Whoops,
3 2 divided by 2 equals 8 66 remainder 0 because it was even do my spacing i did my spacing
then we’ll divide again 866 divided by 2 i don’t know maybe my spacing is kind of dumb maybe i
should have spaced the numbers and not spaced the operator that’s probably better okay so 866 divided
433, 433, and it was even, so the remainder is zero.
And then, 433, okay, so 433 divided by two.
I’m getting tired of this.
I don’t know if you can tell.
216, so 433 divided by two is going to be equal to 216,
and then remainder one.
Space that out.
Oh, I messed that up again, okay.
And then space those out, and then everything is good.
those out and then everything is good okay so then 216 divided by two and of
course I’m just doing this again and again and again I hope this is not too
boring but I hope you’re following along another good tip that I like to give
people when they’re learning new things is do not make the mistake of
accidentally memorizing a handful of examples try to find as many examples as
you possibly can and every time you practice use a different example that
way you will actually learn how to do the thing instead of accidentally
accidentally memorizing an example. Okay, so 108 divided by two. Maybe I’ll do this again,
but with a smaller number just to make things faster. It’s going to be 54,
remainder zero, and then 54 divided by two. I guess I can just do this in my head. I don’t
really trust myself, so I’m going to do it over here. Okay, 24 remainder zero, because it was
even and then we’ll do 27 over here that’s definitely going to be a remainder one so that’s
going to be like probably 13 remainder one i don’t trust myself i’m gonna do it for real
27 divided by 2 13 remainder 1 and then put the 13 there 13 divided by 2 is
um 6 remainder 1 oh no i’m losing it okay 6 remainder 1
for double checking. I am honestly not like an internal mind math whiz. And then we do
six divided by two, that’s just going to be three remainder zero. And then we’ll do
three divided by two is going to be, you know, one because only one of the twos can fit there.
And then one remainder one. And then we have one left over. So we’ll say one divided by two,
we can’t actually fit, you know, any twos into the one. So it’s going to be zero.
so it’s going to be zero remainder one and now at this point remember we’re just carrying over
the quotient result we’re not carrying over the remainder so if I carry this over here
zero divided by two the number is always going to just be zero remainder zero no matter how many
times now no matter how many times we carry this down so we know we’re done when this number that
we’re dividing is a zero we’re just totally finished so now I’m just going to omit that
Well, maybe I’ll leave one up there just to kind of prove a point.
Think about this, if this is actually going to be zeros forever, which side of the number
string would the zeros go on so that no matter how many zeros you computed, the actual result
wouldn’t change?
For example, if I had this original decimal number and I decided to say, all right, I’m
going to add some zeros to it without changing the result.
then it definitely changes what number that is, right?
The value is now multiplied by a thousand.
But if I put the zeros on the left,
then the number doesn’t actually change.
These are junk zeros.
They don’t mean anything or they mean nothing.
So that means wherever the endless zeros are
is actually the left side of the binary string
that you’re trying to make.
Think about it.
You know, we’re not going to put a bunch of zeros
on the right side of a binary string
we’d be increasing the size dramatically just based on our whims of how many times we tried
to divide a zero.
Instead if we stick the numbers on the left side, then the result doesn’t change so it’s
totally fine.
Which means if you kind of tilt your head to the left, that’s the number, not to the
right.
So that means you know probably intuitively you might have been thinking oh the first
number, the first remainder we got that was going to be the first digit and then we work
our way to the right.
we work our way to the right no no no actually it’s backwards we have to reverse it so i’m going
to go ahead and um you know you can you can if you want to you know you can start at the bottom
and work your way up and then just write the binary string correctly sometimes i’d like to
start from the top and then reverse the string later just as a little brain exercise so i’ll go
one two three starting from the top one one two three one one two three one one zero one one
And then I’ll reverse it.
I’ll say 1101100010001000.
And because I just did it this way, this provides a nice opportunity to double check your work
because it’s really easy to get things like this wrong.
I get things wrong all the time.
And so if you can figure out a way to double check your work in two or three different ways,
you reduce the chances of being wrong.
It takes a little more time, but it’s a really good idea when you’re actually doing work
or like you’re taking an exam or whatever.
an exam or whatever check your work in multiple different ways so now that I’ve done it in
the first way I’m going to do it from the bottom up just to see if I was right so I’m
going to go one one zero one one zero zero zero one zero zero zero one zero zero zero
does it match it seems to match so I’m pretty confident that this is the correct number let’s
just punch it in real fast I’m going to punch it in on my personal calculator here real
I’m just going to copy this to my outside calculator just to prove to myself that it works.
55432.
Okay, so this is indeed the correct answer.
We now understand how to convert from decimal to binary.
It’s not too bad, right?
Let’s do another number just for fun, just something really small.
Let’s go 632.
Okay, whoops, nope, nope, nope.
Let’s do another tab.
We’ll say decimal 632 so that this is faster.
We start with 632.
We divide it by 2.
632 we divide it by 2 the result is going to be oh can I guess this 350 and then like a 15 and then
a one one I don’t know if that’s going to be right remainder zero let me see if I can punch this up
632 divided by zero I oh I blew it oh I was thinking of okay this is why I use a calculator
316 divided by 2 is going to be, I thought I was so cool too, like, oh, everyone watching
is going to be so impressed that I did this in my mind.
Nope.
So we do 316 divided by 2, it’s going to be 158 remainder 0.
So 158 divided by 2, that’s going to be, okay, that’s 75 plus 4, I guarantee it.
So I’m going to do 79, 79 remainder 0.
Let me see if I’m right.
Oh gosh, this is going to be embarrassing if I get it wrong.
79, okay.
So then, now we’re gonna do 79 divided by two.
Whoops, I spaced poorly.
79 divided by two is basically gonna be 39 remainder one.
We know it’s remainder one,
cause you know, 79 is odd.
If it was 80 divided by two, it would’ve been 40.
So let’s just double check real fast
to make sure that we’re getting it right.
It’s easy to get things wrong
if you’re not double checking yourself.
39, okay, so then we’ll do 39 divided by two.
divided by 2
well that’s just going to be 20 remainder 1
am I right about that? I don’t know
let’s see
39 divided by 2
oh I blew it
what was I thinking?
of course it’s going to be at least 40 if it’s 20
totally blew it
so 19 divided by 2
ok so I’m looking for a lower number not a higher number
so 18 so that’s 9
let me see 9 remainder 1
am I right?
Am I right? By the way all these shenanigans that I’m doing right now are exactly how I’m gonna end up with the wrong result
And have to do this whole thing all over again from scratch, but hey at least it will be more brain exercise
Okay, so 9 divided by 2
I’m gonna say 4 remainder 1 because it’s odd
We’ll do 9 divided by 2 just to double check and then we’ll say 4 divided by 2 is
think I need to double check it although I probably should anyway 2 divided by 2 is going to be 1
remainder 0 okay we have a 1 so we actually have to do this one more step 1 divided by 2 equals
1 remainder 0 oh sorry sorry sorry sorry 0 remainder 0 otherwise that would have been
infinity 1s for no reason at all so 0 remainder 0 sorry remainder 1
Then finally, we’re down to 0 divided by 2 equals just 0, remainder 0.
And then we’re finished.
Okay.
Let me do it the first way where I go from top to bottom, then reverse it.
1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 1, 2, 3, 4.
Then I’ll try to reverse that.
1, 2, 3, 4, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3.
Okay.
Then I’ll do it from the bottom up.
1, 2, 3, 4, 1, 0, 0, 1, 2, 3, 4, 1, 2, 3.
two, three, do these two match?
Yes, they do.
Okay, I think we’ve successfully done this.
We’re now semi-experts at converting decimal to binary.
Thank you for watching.
I hope you enjoyed this video.
I hope you learned a little bit of stuff and had a little bit of fun.
I’ll see you in the next video.
Hey, everybody.
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