WEBVTT

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

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going to be about converting
decimal numbers into binary

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

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

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exploit the fundamental property
of the binary number system that

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

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start with a simple example.

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

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

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Because 2 * 7 only makes a 14.

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So I still need to add 1 as a

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

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and again I have got a remainder

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

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

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

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

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sequence here. The remainder
sequence when you recording it,

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

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

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

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

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recording I need to start from.

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

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difference, because these are
all digits of ones.

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

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Another thing is you cannot stop
your division here because this

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

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

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here, so that's the last last

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

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

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We can check it going backwards
simply just putting the place

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

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familiar with the method that
you carry on doing these double

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

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

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

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

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no remainders. Again 12 / 2
gives me 6.

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

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

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

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

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

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

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SO12 four 816 and 16 + 8
is indeed 24.

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Next example.

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

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

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

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

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

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remainder of 1 again do the

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

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

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

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

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to remainder 0.

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

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

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forget we need to copy down up.

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Is 1.

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1234 zeros and one
one in binary. Just

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quickly double check.

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One

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248-1632
6464 + 3 makes 67, so

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I'm happy because the
answer is correct.

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Next example 89
again.

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

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

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

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

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

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22 is 11.

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

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

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

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

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remainder. Remember I need to

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finish. Up with this zero here.

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And again I need to copy
the digits bottom up.

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So 89.
In decimal is

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1011001 in binary.

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

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The last example for using the
division method to convert

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

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

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

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

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

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of 70 is 30.

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

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

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Divide that by two
remainder. Again will be 0

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

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

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

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altogether this is 68.

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

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

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

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

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

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because half of 30 is 15.

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

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

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

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

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

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again, and the answer is two 2 /

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

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

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

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the answer for the division.

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So copy that there.

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Did bottom up.

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

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

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

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correct number that we wanted,

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so 12. Four
816-3264 hundred 28256.

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So what I've
got here is

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256. Add 16
so 256 +

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10 is 266.

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+6 that is indeed
272.

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

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division method to convert
decimal numbers to binary

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

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you some extra practice
questions that you can do

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

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

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

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are the practice questions.

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And here are the answers.