Welcome to the 4th video on the
binary numbers. This video again

going to be about converting
decimal numbers into binary

numbers, but this video will use
a different method. This method

is called the division method.
In this method, we're going to

exploit the fundamental property
of the binary number system that

every single place value there
is a multiple of two. So let's

start with a simple example.

Let's say 15. So what does 15 in
decimal look like in binary? So

let's divide 15 by 215 / 2 gives
me 7 and the remainder is 1.

Because 2 * 7 only makes a 14.

So I still need to add 1 as a

remainder then. Divide the
number again so 7 / 2 gives me 3

and again I have got a remainder

of 1. Because 2 * 3 is
6 + 1, makes decelem 3 / 2 gives

me one because 1 * 2 is 2. But
I still got a remainder of 1 and

then 1. / 2 gives me zero and
the remainder is 1.

Now there is 1 trick here, which
is once you've got your number

sequence here. The remainder
sequence when you recording it,

you need to record it from
bottom up. Why is that? Well,

when I'm first dividing by two
here, I'm only dividing by the

smallest place value. Then I'm
dividing by a bigger place for

you and this one is the biggest
place. Why that's why when I'm

recording I need to start from.

Bottom up now, in this
particular case, it will make no

difference, because these are
all digits of ones.

But in other examples you will
see that there is a difference.

Another thing is you cannot stop
your division here because this

means that you haven't divided
by all the necessary place

values. You have to keep going
until you get an answer of 0

here, so that's the last last

step. So 15 in decimal is 1111
in binary. Now if we want to be

really sure about that, we've
done the conversion correctly.

We can check it going backwards
simply just putting the place

values on top of the number. I
suggest the until you become

familiar with the method that
you carry on doing these double

checks. So that's 1248 and I
know that 8 + 2 makes 10.

And I knew that 4 + 1 makes 5,
so yes indeed this is 15.

Let's look at the next timestamp
or the next example is 24, So

what is 24 / 224 / 2 gives
me 12 and in this case I've got

no remainders. Again 12 / 2
gives me 6.

No remainders, 6 / 2 gives
ME3, no remainders, and 3 / 2

gives me one remainder one.
And don't forget the last Step

1 / 2 gives me zero and the
remainder is 1 again.

Copy the digits bottom up so 24
in decimal equals 11000 in

binary. Again, let's do a quick
check if this answer is actually

correct or not. So put the place
values on top of each digits,

SO12 four 816 and 16 + 8
is indeed 24.

Next example.

6767 / 2 now the number starts
to get a little bit bigger than

the division. Gets a little bit
trickier, but there is always

something that you can use. How
many twos go into six while

three Dash 4 twos into 60 will
be 30 something? And how many

twos goes into seven while three
because 3 * 3 Six? So I've got a

remainder of 1 again do the

division. 30 / 2 is
15 and 3 / 2 is

1 so this will be 16
and remainder one the double of

16 is 32. Add one gives
3316 / 2 makes, 8 remainders

zero 8 / 2 gives 4
remainder zero 4 / 2 gives

to remainder 0.

Do you think that divide by two
gives you one remainder 0 and 1

/ 2 is zero, remainder one so
67 in decimal is. Again, don't

forget we need to copy down up.

Is 1.

1234 zeros and one
one in binary. Just

quickly double check.

One

248-1632
6464 + 3 makes 67, so

I'm happy because the
answer is correct.

Next example 89
again.

I need to divide it by two so 89
/ 2. Well, this is an odd number

so I know that the remainder
will be one. So how about

instead of 89 dividing 88 by two
while 88 / 2 is 44, so that's

slightly easier to do 44 / 2 is
22. Remember I'm just having it

and the remainder will be zero
22 / 2 gives me 11 again half of

22 is 11.

Remainder zero 11. / 2 again.
The remainder will be one and if

I take 1 from 11 that gives me
10. So 11 / 2 is 5 and remainder

one 5 / 2 is 2 remainder one
because 2 * 2 is 4 + 1 makes

a five 2 / 2 is 1 no remainder
and 1 / 2 is zero with one

remainder. Remember I need to

finish. Up with this zero here.

And again I need to copy
the digits bottom up.

So 89.
In decimal is

1011001 in binary.

I'm going to leave you to check
if the answer is correct.

The last example for using the
division method to convert

decimal to binary numbers will
be 272. Now divide that by two.

I know this is an even number,
therefore my remainder will be

0, but 272 is quite a big number
to have in my head. So what I'm

going to do I'm going to
partition it so I'm going to

have 201st half of 200 is 100,
then I'm going to half 70 half

of 70 is 30.

Five and I'm gonna half two half
of two is 1, so the half of 272

is 136, which is the sum of all
these hearts. So again.

Divide that by two
remainder. Again will be 0

because it's again an even
number. So what's the half

of 100 half of 100 is 50,
what the half of 30 half of

30 is 15, and what's the
half of 6 is 3? So

altogether this is 68.

Divide that by two. That's going
to give me a remainder of 0,

because that's an even number
and what's the half of 68 while

half of 60 is 30, an half of
eight is 4, so this will be 34.

Divide that by two. The
remainder will be 0 because this

is an even #34 is might not be
as easy to half as 68 was

because half of 30 is 15.

And half of four is 2, so that
gives me 1717 / 2. That's an odd

number, so my remainder will be
one. And if I take that, the

remainder away from the number I
will left with 16 and half of 16

is 8 zero, 8 / 2 again. The
remainder will be 0 because it's

an even number. Half of that is
four 4 /, 2 remainder will be 0

again, and the answer is two 2 /

2. Is 1 remainder is 0 and 1 / 2
is zero. Remainder of 1 again I

have to stress that you haven't
finished at this point of the

algorithm because you need to go
back then you have got zero as

the answer for the division.

So copy that there.

Did bottom up.

372 in decimal is equal to 1
followed by three zeros and one

followed by 4 zeros in binary.
Now that number looks slightly

suspicious, so let's double
check that this is actually the

correct number that we wanted,

so 12. Four
816-3264 hundred 28256.

So what I've
got here is

256. Add 16
so 256 +

10 is 266.

+6 that is indeed
272.

So these are the examples to
show you how to use the

division method to convert
decimal numbers to binary

numbers in the next few
minutes. I'm going to show

you some extra practice
questions that you can do

yourself and then I will show
you the answers. I suggest

that you post the video while
you're carrying out the

calculations so your fan
won't be spoiled, so these

are the practice questions.

And here are the answers.