1
00:00:14,590 --> 00:00:19,078
Welcome to the 4th video on the
binary numbers. This video again

2
00:00:19,078 --> 00:00:22,444
going to be about converting
decimal numbers into binary

3
00:00:22,444 --> 00:00:26,558
numbers, but this video will use
a different method. This method

4
00:00:26,558 --> 00:00:30,672
is called the division method.
In this method, we're going to

5
00:00:30,672 --> 00:00:34,412
exploit the fundamental property
of the binary number system that

6
00:00:34,412 --> 00:00:38,900
every single place value there
is a multiple of two. So let's

7
00:00:38,900 --> 00:00:40,770
start with a simple example.

8
00:00:41,430 --> 00:00:47,100
Let's say 15. So what does 15 in
decimal look like in binary? So

9
00:00:47,100 --> 00:00:53,175
let's divide 15 by 215 / 2 gives
me 7 and the remainder is 1.

10
00:00:53,175 --> 00:00:56,415
Because 2 * 7 only makes a 14.

11
00:00:57,300 --> 00:01:00,513
So I still need to add 1 as a

12
00:01:00,513 --> 00:01:06,086
remainder then. Divide the
number again so 7 / 2 gives me 3

13
00:01:06,086 --> 00:01:08,788
and again I have got a remainder

14
00:01:08,788 --> 00:01:16,410
of 1. Because 2 * 3 is
6 + 1, makes decelem 3 / 2 gives

15
00:01:16,410 --> 00:01:23,635
me one because 1 * 2 is 2. But
I still got a remainder of 1 and

16
00:01:23,635 --> 00:01:28,735
then 1. / 2 gives me zero and
the remainder is 1.

17
00:01:29,760 --> 00:01:34,947
Now there is 1 trick here, which
is once you've got your number

18
00:01:34,947 --> 00:01:38,538
sequence here. The remainder
sequence when you recording it,

19
00:01:38,538 --> 00:01:43,326
you need to record it from
bottom up. Why is that? Well,

20
00:01:43,326 --> 00:01:48,114
when I'm first dividing by two
here, I'm only dividing by the

21
00:01:48,114 --> 00:01:52,503
smallest place value. Then I'm
dividing by a bigger place for

22
00:01:52,503 --> 00:01:57,690
you and this one is the biggest
place. Why that's why when I'm

23
00:01:57,690 --> 00:02:00,084
recording I need to start from.

24
00:02:00,180 --> 00:02:03,898
Bottom up now, in this
particular case, it will make no

25
00:02:03,898 --> 00:02:06,602
difference, because these are
all digits of ones.

26
00:02:07,590 --> 00:02:11,766
But in other examples you will
see that there is a difference.

27
00:02:11,766 --> 00:02:15,594
Another thing is you cannot stop
your division here because this

28
00:02:15,594 --> 00:02:19,074
means that you haven't divided
by all the necessary place

29
00:02:19,074 --> 00:02:23,598
values. You have to keep going
until you get an answer of 0

30
00:02:23,598 --> 00:02:25,686
here, so that's the last last

31
00:02:25,686 --> 00:02:32,770
step. So 15 in decimal is 1111
in binary. Now if we want to be

32
00:02:32,770 --> 00:02:36,640
really sure about that, we've
done the conversion correctly.

33
00:02:36,640 --> 00:02:41,370
We can check it going backwards
simply just putting the place

34
00:02:41,370 --> 00:02:46,530
values on top of the number. I
suggest the until you become

35
00:02:46,530 --> 00:02:51,260
familiar with the method that
you carry on doing these double

36
00:02:51,260 --> 00:02:56,850
checks. So that's 1248 and I
know that 8 + 2 makes 10.

37
00:02:57,060 --> 00:03:02,250
And I knew that 4 + 1 makes 5,
so yes indeed this is 15.

38
00:03:04,460 --> 00:03:10,414
Let's look at the next timestamp
or the next example is 24, So

39
00:03:10,414 --> 00:03:17,742
what is 24 / 224 / 2 gives
me 12 and in this case I've got

40
00:03:17,742 --> 00:03:21,864
no remainders. Again 12 / 2
gives me 6.

41
00:03:22,460 --> 00:03:28,895
No remainders, 6 / 2 gives
ME3, no remainders, and 3 / 2

42
00:03:28,895 --> 00:03:34,340
gives me one remainder one.
And don't forget the last Step

43
00:03:34,340 --> 00:03:40,280
1 / 2 gives me zero and the
remainder is 1 again.

44
00:03:41,330 --> 00:03:48,074
Copy the digits bottom up so 24
in decimal equals 11000 in

45
00:03:48,074 --> 00:03:54,818
binary. Again, let's do a quick
check if this answer is actually

46
00:03:54,818 --> 00:04:02,124
correct or not. So put the place
values on top of each digits,

47
00:04:02,124 --> 00:04:07,744
SO12 four 816 and 16 + 8
is indeed 24.

48
00:04:11,040 --> 00:04:12,270
Next example.

49
00:04:13,800 --> 00:04:19,708
6767 / 2 now the number starts
to get a little bit bigger than

50
00:04:19,708 --> 00:04:24,350
the division. Gets a little bit
trickier, but there is always

51
00:04:24,350 --> 00:04:29,414
something that you can use. How
many twos go into six while

52
00:04:29,414 --> 00:04:34,900
three Dash 4 twos into 60 will
be 30 something? And how many

53
00:04:34,900 --> 00:04:41,230
twos goes into seven while three
because 3 * 3 Six? So I've got a

54
00:04:41,230 --> 00:04:43,762
remainder of 1 again do the

55
00:04:43,762 --> 00:04:51,030
division. 30 / 2 is
15 and 3 / 2 is

56
00:04:51,030 --> 00:04:58,086
1 so this will be 16
and remainder one the double of

57
00:04:58,086 --> 00:05:05,142
16 is 32. Add one gives
3316 / 2 makes, 8 remainders

58
00:05:05,142 --> 00:05:12,198
zero 8 / 2 gives 4
remainder zero 4 / 2 gives

59
00:05:12,198 --> 00:05:13,962
to remainder 0.

60
00:05:14,340 --> 00:05:21,998
Do you think that divide by two
gives you one remainder 0 and 1

61
00:05:21,998 --> 00:05:29,109
/ 2 is zero, remainder one so
67 in decimal is. Again, don't

62
00:05:29,109 --> 00:05:32,938
forget we need to copy down up.

63
00:05:34,270 --> 00:05:35,400
Is 1.

64
00:05:37,230 --> 00:05:43,710
1234 zeros and one
one in binary. Just

65
00:05:43,710 --> 00:05:46,140
quickly double check.

66
00:05:47,130 --> 00:05:49,615
One

67
00:05:49,615 --> 00:05:56,610
248-1632
6464 + 3 makes 67, so

68
00:05:56,610 --> 00:06:00,740
I'm happy because the
answer is correct.

69
00:06:02,770 --> 00:06:07,478
Next example 89
again.

70
00:06:08,980 --> 00:06:16,307
I need to divide it by two so 89
/ 2. Well, this is an odd number

71
00:06:16,307 --> 00:06:21,479
so I know that the remainder
will be one. So how about

72
00:06:21,479 --> 00:06:27,944
instead of 89 dividing 88 by two
while 88 / 2 is 44, so that's

73
00:06:27,944 --> 00:06:33,978
slightly easier to do 44 / 2 is
22. Remember I'm just having it

74
00:06:33,978 --> 00:06:40,443
and the remainder will be zero
22 / 2 gives me 11 again half of

75
00:06:40,443 --> 00:06:41,736
22 is 11.

76
00:06:41,810 --> 00:06:47,452
Remainder zero 11. / 2 again.
The remainder will be one and if

77
00:06:47,452 --> 00:06:54,830
I take 1 from 11 that gives me
10. So 11 / 2 is 5 and remainder

78
00:06:54,830 --> 00:07:02,208
one 5 / 2 is 2 remainder one
because 2 * 2 is 4 + 1 makes

79
00:07:02,208 --> 00:07:09,586
a five 2 / 2 is 1 no remainder
and 1 / 2 is zero with one

80
00:07:09,586 --> 00:07:11,756
remainder. Remember I need to

81
00:07:11,756 --> 00:07:13,640
finish. Up with this zero here.

82
00:07:14,520 --> 00:07:17,360
And again I need to copy
the digits bottom up.

83
00:07:18,800 --> 00:07:26,040
So 89.
In decimal is

84
00:07:26,040 --> 00:07:29,850
1011001 in binary.

85
00:07:30,580 --> 00:07:33,100
I'm going to leave you to check
if the answer is correct.

86
00:07:35,570 --> 00:07:39,230
The last example for using the
division method to convert

87
00:07:39,230 --> 00:07:43,622
decimal to binary numbers will
be 272. Now divide that by two.

88
00:07:43,622 --> 00:07:48,014
I know this is an even number,
therefore my remainder will be

89
00:07:48,014 --> 00:07:53,870
0, but 272 is quite a big number
to have in my head. So what I'm

90
00:07:53,870 --> 00:07:58,262
going to do I'm going to
partition it so I'm going to

91
00:07:58,262 --> 00:08:03,386
have 201st half of 200 is 100,
then I'm going to half 70 half

92
00:08:03,386 --> 00:08:04,850
of 70 is 30.

93
00:08:04,940 --> 00:08:11,740
Five and I'm gonna half two half
of two is 1, so the half of 272

94
00:08:11,740 --> 00:08:16,840
is 136, which is the sum of all
these hearts. So again.

95
00:08:17,800 --> 00:08:21,661
Divide that by two
remainder. Again will be 0

96
00:08:21,661 --> 00:08:25,951
because it's again an even
number. So what's the half

97
00:08:25,951 --> 00:08:31,957
of 100 half of 100 is 50,
what the half of 30 half of

98
00:08:31,957 --> 00:08:37,105
30 is 15, and what's the
half of 6 is 3? So

99
00:08:37,105 --> 00:08:38,821
altogether this is 68.

100
00:08:40,780 --> 00:08:45,226
Divide that by two. That's going
to give me a remainder of 0,

101
00:08:45,226 --> 00:08:49,330
because that's an even number
and what's the half of 68 while

102
00:08:49,330 --> 00:08:54,802
half of 60 is 30, an half of
eight is 4, so this will be 34.

103
00:08:55,780 --> 00:09:00,125
Divide that by two. The
remainder will be 0 because this

104
00:09:00,125 --> 00:09:06,050
is an even #34 is might not be
as easy to half as 68 was

105
00:09:06,050 --> 00:09:08,420
because half of 30 is 15.

106
00:09:09,590 --> 00:09:15,702
And half of four is 2, so that
gives me 1717 / 2. That's an odd

107
00:09:15,702 --> 00:09:20,668
number, so my remainder will be
one. And if I take that, the

108
00:09:20,668 --> 00:09:26,016
remainder away from the number I
will left with 16 and half of 16

109
00:09:26,016 --> 00:09:31,364
is 8 zero, 8 / 2 again. The
remainder will be 0 because it's

110
00:09:31,364 --> 00:09:37,094
an even number. Half of that is
four 4 /, 2 remainder will be 0

111
00:09:37,094 --> 00:09:40,150
again, and the answer is two 2 /

112
00:09:40,150 --> 00:09:46,518
2. Is 1 remainder is 0 and 1 / 2
is zero. Remainder of 1 again I

113
00:09:46,518 --> 00:09:50,934
have to stress that you haven't
finished at this point of the

114
00:09:50,934 --> 00:09:55,718
algorithm because you need to go
back then you have got zero as

115
00:09:55,718 --> 00:09:57,558
the answer for the division.

116
00:09:58,270 --> 00:10:00,038
So copy that there.

117
00:10:00,110 --> 00:10:01,598
Did bottom up.

118
00:10:02,870 --> 00:10:09,734
372 in decimal is equal to 1
followed by three zeros and one

119
00:10:09,734 --> 00:10:15,542
followed by 4 zeros in binary.
Now that number looks slightly

120
00:10:15,542 --> 00:10:20,822
suspicious, so let's double
check that this is actually the

121
00:10:20,822 --> 00:10:23,462
correct number that we wanted,

122
00:10:23,462 --> 00:10:29,592
so 12. Four
816-3264 hundred 28256.

123
00:10:29,592 --> 00:10:35,970
So what I've
got here is

124
00:10:35,970 --> 00:10:42,348
256. Add 16
so 256 +

125
00:10:42,348 --> 00:10:45,537
10 is 266.

126
00:10:47,160 --> 00:10:51,270
+6 that is indeed
272.

127
00:10:53,820 --> 00:10:57,732
So these are the examples to
show you how to use the

128
00:10:57,732 --> 00:11:00,340
division method to convert
decimal numbers to binary

129
00:11:00,340 --> 00:11:03,600
numbers in the next few
minutes. I'm going to show

130
00:11:03,600 --> 00:11:06,534
you some extra practice
questions that you can do

131
00:11:06,534 --> 00:11:10,120
yourself and then I will show
you the answers. I suggest

132
00:11:10,120 --> 00:11:13,380
that you post the video while
you're carrying out the

133
00:11:13,380 --> 00:11:16,314
calculations so your fan
won't be spoiled, so these

134
00:11:16,314 --> 00:11:17,618
are the practice questions.

135
00:11:23,480 --> 00:11:25,060
And here are the answers.