0:00:14.590,0:00:19.078
Welcome to the 4th video on the[br]binary numbers. This video again

0:00:19.078,0:00:22.444
going to be about converting[br]decimal numbers into binary

0:00:22.444,0:00:26.558
numbers, but this video will use[br]a different method. This method

0:00:26.558,0:00:30.672
is called the division method.[br]In this method, we're going to

0:00:30.672,0:00:34.412
exploit the fundamental property[br]of the binary number system that

0:00:34.412,0:00:38.900
every single place value there[br]is a multiple of two. So let's

0:00:38.900,0:00:40.770
start with a simple example.

0:00:41.430,0:00:47.100
Let's say 15. So what does 15 in[br]decimal look like in binary? So

0:00:47.100,0:00:53.175
let's divide 15 by 215 / 2 gives[br]me 7 and the remainder is 1.

0:00:53.175,0:00:56.415
Because 2 * 7 only makes a 14.

0:00:57.300,0:01:00.513
So I still need to add 1 as a

0:01:00.513,0:01:06.086
remainder then. Divide the[br]number again so 7 / 2 gives me 3

0:01:06.086,0:01:08.788
and again I have got a remainder

0:01:08.788,0:01:16.410
of 1. Because 2 * 3 is[br]6 + 1, makes decelem 3 / 2 gives

0:01:16.410,0:01:23.635
me one because 1 * 2 is 2. But[br]I still got a remainder of 1 and

0:01:23.635,0:01:28.735
then 1. / 2 gives me zero and[br]the remainder is 1.

0:01:29.760,0:01:34.947
Now there is 1 trick here, which[br]is once you've got your number

0:01:34.947,0:01:38.538
sequence here. The remainder[br]sequence when you recording it,

0:01:38.538,0:01:43.326
you need to record it from[br]bottom up. Why is that? Well,

0:01:43.326,0:01:48.114
when I'm first dividing by two[br]here, I'm only dividing by the

0:01:48.114,0:01:52.503
smallest place value. Then I'm[br]dividing by a bigger place for

0:01:52.503,0:01:57.690
you and this one is the biggest[br]place. Why that's why when I'm

0:01:57.690,0:02:00.084
recording I need to start from.

0:02:00.180,0:02:03.898
Bottom up now, in this[br]particular case, it will make no

0:02:03.898,0:02:06.602
difference, because these are[br]all digits of ones.

0:02:07.590,0:02:11.766
But in other examples you will[br]see that there is a difference.

0:02:11.766,0:02:15.594
Another thing is you cannot stop[br]your division here because this

0:02:15.594,0:02:19.074
means that you haven't divided[br]by all the necessary place

0:02:19.074,0:02:23.598
values. You have to keep going[br]until you get an answer of 0

0:02:23.598,0:02:25.686
here, so that's the last last

0:02:25.686,0:02:32.770
step. So 15 in decimal is 1111[br]in binary. Now if we want to be

0:02:32.770,0:02:36.640
really sure about that, we've[br]done the conversion correctly.

0:02:36.640,0:02:41.370
We can check it going backwards[br]simply just putting the place

0:02:41.370,0:02:46.530
values on top of the number. I[br]suggest the until you become

0:02:46.530,0:02:51.260
familiar with the method that[br]you carry on doing these double

0:02:51.260,0:02:56.850
checks. So that's 1248 and I[br]know that 8 + 2 makes 10.

0:02:57.060,0:03:02.250
And I knew that 4 + 1 makes 5,[br]so yes indeed this is 15.

0:03:04.460,0:03:10.414
Let's look at the next timestamp[br]or the next example is 24, So

0:03:10.414,0:03:17.742
what is 24 / 224 / 2 gives[br]me 12 and in this case I've got

0:03:17.742,0:03:21.864
no remainders. Again 12 / 2[br]gives me 6.

0:03:22.460,0:03:28.895
No remainders, 6 / 2 gives[br]ME3, no remainders, and 3 / 2

0:03:28.895,0:03:34.340
gives me one remainder one.[br]And don't forget the last Step

0:03:34.340,0:03:40.280
1 / 2 gives me zero and the[br]remainder is 1 again.

0:03:41.330,0:03:48.074
Copy the digits bottom up so 24[br]in decimal equals 11000 in

0:03:48.074,0:03:54.818
binary. Again, let's do a quick[br]check if this answer is actually

0:03:54.818,0:04:02.124
correct or not. So put the place[br]values on top of each digits,

0:04:02.124,0:04:07.744
SO12 four 816 and 16 + 8[br]is indeed 24.

0:04:11.040,0:04:12.270
Next example.

0:04:13.800,0:04:19.708
6767 / 2 now the number starts[br]to get a little bit bigger than

0:04:19.708,0:04:24.350
the division. Gets a little bit[br]trickier, but there is always

0:04:24.350,0:04:29.414
something that you can use. How[br]many twos go into six while

0:04:29.414,0:04:34.900
three Dash 4 twos into 60 will[br]be 30 something? And how many

0:04:34.900,0:04:41.230
twos goes into seven while three[br]because 3 * 3 Six? So I've got a

0:04:41.230,0:04:43.762
remainder of 1 again do the

0:04:43.762,0:04:51.030
division. 30 / 2 is[br]15 and 3 / 2 is

0:04:51.030,0:04:58.086
1 so this will be 16[br]and remainder one the double of

0:04:58.086,0:05:05.142
16 is 32. Add one gives[br]3316 / 2 makes, 8 remainders

0:05:05.142,0:05:12.198
zero 8 / 2 gives 4[br]remainder zero 4 / 2 gives

0:05:12.198,0:05:13.962
to remainder 0.

0:05:14.340,0:05:21.998
Do you think that divide by two[br]gives you one remainder 0 and 1

0:05:21.998,0:05:29.109
/ 2 is zero, remainder one so[br]67 in decimal is. Again, don't

0:05:29.109,0:05:32.938
forget we need to copy down up.

0:05:34.270,0:05:35.400
Is 1.

0:05:37.230,0:05:43.710
1234 zeros and one[br]one in binary. Just

0:05:43.710,0:05:46.140
quickly double check.

0:05:47.130,0:05:49.615
One

0:05:49.615,0:05:56.610
248-1632[br]6464 + 3 makes 67, so

0:05:56.610,0:06:00.740
I'm happy because the[br]answer is correct.

0:06:02.770,0:06:07.478
Next example 89[br]again.

0:06:08.980,0:06:16.307
I need to divide it by two so 89[br]/ 2. Well, this is an odd number

0:06:16.307,0:06:21.479
so I know that the remainder[br]will be one. So how about

0:06:21.479,0:06:27.944
instead of 89 dividing 88 by two[br]while 88 / 2 is 44, so that's

0:06:27.944,0:06:33.978
slightly easier to do 44 / 2 is[br]22. Remember I'm just having it

0:06:33.978,0:06:40.443
and the remainder will be zero[br]22 / 2 gives me 11 again half of

0:06:40.443,0:06:41.736
22 is 11.

0:06:41.810,0:06:47.452
Remainder zero 11. / 2 again.[br]The remainder will be one and if

0:06:47.452,0:06:54.830
I take 1 from 11 that gives me[br]10. So 11 / 2 is 5 and remainder

0:06:54.830,0:07:02.208
one 5 / 2 is 2 remainder one[br]because 2 * 2 is 4 + 1 makes

0:07:02.208,0:07:09.586
a five 2 / 2 is 1 no remainder[br]and 1 / 2 is zero with one

0:07:09.586,0:07:11.756
remainder. Remember I need to

0:07:11.756,0:07:13.640
finish. Up with this zero here.

0:07:14.520,0:07:17.360
And again I need to copy[br]the digits bottom up.

0:07:18.800,0:07:26.040
So 89.[br]In decimal is

0:07:26.040,0:07:29.850
1011001 in binary.

0:07:30.580,0:07:33.100
I'm going to leave you to check[br]if the answer is correct.

0:07:35.570,0:07:39.230
The last example for using the[br]division method to convert

0:07:39.230,0:07:43.622
decimal to binary numbers will[br]be 272. Now divide that by two.

0:07:43.622,0:07:48.014
I know this is an even number,[br]therefore my remainder will be

0:07:48.014,0:07:53.870
0, but 272 is quite a big number[br]to have in my head. So what I'm

0:07:53.870,0:07:58.262
going to do I'm going to[br]partition it so I'm going to

0:07:58.262,0:08:03.386
have 201st half of 200 is 100,[br]then I'm going to half 70 half

0:08:03.386,0:08:04.850
of 70 is 30.

0:08:04.940,0:08:11.740
Five and I'm gonna half two half[br]of two is 1, so the half of 272

0:08:11.740,0:08:16.840
is 136, which is the sum of all[br]these hearts. So again.

0:08:17.800,0:08:21.661
Divide that by two[br]remainder. Again will be 0

0:08:21.661,0:08:25.951
because it's again an even[br]number. So what's the half

0:08:25.951,0:08:31.957
of 100 half of 100 is 50,[br]what the half of 30 half of

0:08:31.957,0:08:37.105
30 is 15, and what's the[br]half of 6 is 3? So

0:08:37.105,0:08:38.821
altogether this is 68.

0:08:40.780,0:08:45.226
Divide that by two. That's going[br]to give me a remainder of 0,

0:08:45.226,0:08:49.330
because that's an even number[br]and what's the half of 68 while

0:08:49.330,0:08:54.802
half of 60 is 30, an half of[br]eight is 4, so this will be 34.

0:08:55.780,0:09:00.125
Divide that by two. The[br]remainder will be 0 because this

0:09:00.125,0:09:06.050
is an even #34 is might not be[br]as easy to half as 68 was

0:09:06.050,0:09:08.420
because half of 30 is 15.

0:09:09.590,0:09:15.702
And half of four is 2, so that[br]gives me 1717 / 2. That's an odd

0:09:15.702,0:09:20.668
number, so my remainder will be[br]one. And if I take that, the

0:09:20.668,0:09:26.016
remainder away from the number I[br]will left with 16 and half of 16

0:09:26.016,0:09:31.364
is 8 zero, 8 / 2 again. The[br]remainder will be 0 because it's

0:09:31.364,0:09:37.094
an even number. Half of that is[br]four 4 /, 2 remainder will be 0

0:09:37.094,0:09:40.150
again, and the answer is two 2 /

0:09:40.150,0:09:46.518
2. Is 1 remainder is 0 and 1 / 2[br]is zero. Remainder of 1 again I

0:09:46.518,0:09:50.934
have to stress that you haven't[br]finished at this point of the

0:09:50.934,0:09:55.718
algorithm because you need to go[br]back then you have got zero as

0:09:55.718,0:09:57.558
the answer for the division.

0:09:58.270,0:10:00.038
So copy that there.

0:10:00.110,0:10:01.598
Did bottom up.

0:10:02.870,0:10:09.734
372 in decimal is equal to 1[br]followed by three zeros and one

0:10:09.734,0:10:15.542
followed by 4 zeros in binary.[br]Now that number looks slightly

0:10:15.542,0:10:20.822
suspicious, so let's double[br]check that this is actually the

0:10:20.822,0:10:23.462
correct number that we wanted,

0:10:23.462,0:10:29.592
so 12. Four[br]816-3264 hundred 28256.

0:10:29.592,0:10:35.970
So what I've[br]got here is

0:10:35.970,0:10:42.348
256. Add 16[br]so 256 +

0:10:42.348,0:10:45.537
10 is 266.

0:10:47.160,0:10:51.270
+6 that is indeed[br]272.

0:10:53.820,0:10:57.732
So these are the examples to[br]show you how to use the

0:10:57.732,0:11:00.340
division method to convert[br]decimal numbers to binary

0:11:00.340,0:11:03.600
numbers in the next few[br]minutes. I'm going to show

0:11:03.600,0:11:06.534
you some extra practice[br]questions that you can do

0:11:06.534,0:11:10.120
yourself and then I will show[br]you the answers. I suggest

0:11:10.120,0:11:13.380
that you post the video while[br]you're carrying out the

0:11:13.380,0:11:16.314
calculations so your fan[br]won't be spoiled, so these

0:11:16.314,0:11:17.618
are the practice questions.

0:11:23.480,0:11:25.060
And here are the answers.