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.