1
00:00:05,500 --> 00:00:10,480
So think about it like this when you need to send a signal to a computer and you need to indicate 1

2
00:00:10,750 --> 00:00:14,390
you apply current, when you want indicate 0

3
00:00:14,410 --> 00:00:16,030
you don't apply current.

4
00:00:16,180 --> 00:00:17,260
Here we have a cable.

5
00:00:17,290 --> 00:00:23,150
It's turned off no current is flowing binary value is 0.

6
00:00:23,200 --> 00:00:24,630
I'll turn that on.

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00:00:24,770 --> 00:00:28,020
So current is now flowing binary value is 1.

8
00:00:28,090 --> 00:00:34,840
We have two states either current or no current two binary values 0 or 1.

9
00:00:35,140 --> 00:00:39,830
So one cable two states either current or no current.

10
00:00:39,850 --> 00:00:47,380
If we extend that now and we've got two cables binary value is currently 0 0 there's no current

11
00:00:47,560 --> 00:00:48,940
on either cable.

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00:00:48,940 --> 00:00:56,230
If I put current on the one binary value is now 0 1 change that current on the left no current on the

13
00:00:56,230 --> 00:01:01,390
right binary value is now 1 0 turn them both on.

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We've got current on two cables binary value is now 1 1.

15
00:01:06,430 --> 00:01:15,930
So we either have no current on both binary value 0 0 or 0 1 or 1 0.

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And lastly 1 1.

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00:01:17,890 --> 00:01:20,640
We have two states either on or off.

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00:01:20,740 --> 00:01:24,700
We have two cables two to the power of two is four.

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00:01:24,910 --> 00:01:31,740
At the moment current is applied the bulb is on that indicates 1 I can turn that off 

20
00:01:31,840 --> 00:01:33,750
that indicates 0.

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00:01:33,790 --> 00:01:42,340
So if I want to send you some numbers I could say 1 0 1 0.

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00:01:42,750 --> 00:01:44,190
And then finally a 1.

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00:01:44,190 --> 00:01:46,470
Let's put the lamp back on again.

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00:01:46,470 --> 00:01:52,360
That's how a computer can send information to another computer or that's how programs are written.

25
00:01:52,410 --> 00:01:59,130
We might write a program in a high-level programming language like Python but as it goes down we end

26
00:01:59,130 --> 00:02:02,010
up doing assembly language.

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00:02:02,010 --> 00:02:07,420
We end up writing 0s and 1s to tell the computer what it needs to do.

28
00:02:07,440 --> 00:02:12,840
Now the important lesson here is we have two states either on or off.

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00:02:12,840 --> 00:02:17,540
If we have one cable we have two states on off on one cable.

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00:02:17,700 --> 00:02:24,840
But if we've got two cables we end up having four states we've either got a 0 0 no current or both cables

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00:02:25,250 --> 00:02:30,760
or 0 1 0 1 0 or 1 1 current on both cables.

32
00:02:30,780 --> 00:02:37,550
So two states two cables means that we end up having four values.

33
00:02:37,650 --> 00:02:44,820
You can write that as 2 x 2 equals 4 or 2 to the power of 2 equals 4.

34
00:02:44,820 --> 00:02:48,330
Two states two cables equals four.

35
00:02:48,330 --> 00:02:53,670
Now don't want to spend too much time on this analogy but let's assume we've got three cables in this

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00:02:53,670 --> 00:02:55,920
example we have three cables.

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00:02:56,070 --> 00:02:59,000
We've got two states current state is off.

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00:02:59,270 --> 00:03:03,180
So the binary value is 0 0 0.

39
00:03:03,180 --> 00:03:13,770
Once again and I won't go through all the combinations we could have 0 0 1 or as an example 1 0 1 or

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00:03:14,040 --> 00:03:15,680
1 1 1.

41
00:03:15,810 --> 00:03:18,330
So we have two states either on or off.

42
00:03:18,330 --> 00:03:20,310
We have three cables.

43
00:03:20,310 --> 00:03:25,530
So 2 x 2 is 8 or 2 to the power 3 is 8.

44
00:03:25,530 --> 00:03:28,970
There are eight different combinations or options here.

45
00:03:28,990 --> 00:03:34,310
Now I won't bore you extending that too much but we could do something very similar.

46
00:03:34,440 --> 00:03:37,640
You tell me what binary value do we have here.

47
00:03:37,650 --> 00:03:43,040
If we've got four cables answer is 0 1 1 1.

48
00:03:43,140 --> 00:03:45,210
How many combinations do we have?

49
00:03:45,210 --> 00:03:47,610
We have two states four cables.

50
00:03:47,610 --> 00:03:56,850
2 x 2 x 2 x 2 = 16 or 2 to the power of 4 = 16, 16 different combinations.

51
00:03:56,850 --> 00:03:59,310
In this example they are all on.

52
00:03:59,310 --> 00:04:03,420
We have two states four cables 16 combinations.

53
00:04:03,990 --> 00:04:08,910
So we've either got no current on the first cable, no current on the second, none on the third none on

54
00:04:08,910 --> 00:04:16,010
the fourth.  Whereas an example no current, no current, no current, current or no current ,no current, current

55
00:04:16,110 --> 00:04:17,130
no current.

56
00:04:17,130 --> 00:04:23,180
And if we go through all the possible combinations we're going to end up having 16 binary values.

57
00:04:23,220 --> 00:04:29,400
So two states are shown over here four cables means 2 to the power of 4.

58
00:04:29,520 --> 00:04:32,340
Sixteen possible combinations.

59
00:04:32,340 --> 00:04:36,550
Again two states four cables gives us 16.

60
00:04:36,720 --> 00:04:44,760
If we've got two states and we've got five cables that would give us 32 or if we have two states and

61
00:04:44,760 --> 00:04:52,530
six cables that gives us 64 combinations. You could manually work this out you could manually go through

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00:04:52,530 --> 00:04:54,090
every combination.

63
00:04:54,210 --> 00:04:55,950
But we're not going to do that.

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00:04:55,950 --> 00:05:01,430
But if you wanted to test this and verify that I'm talking the truth then you could do that.

65
00:05:01,440 --> 00:05:08,950
So just to summarize if we've got two states and one cable 2 to the power of 1 is 2.

66
00:05:09,200 --> 00:05:16,440
So two possible combinations. If we've got two states and two cables that gives us four combinations

67
00:05:16,470 --> 00:05:22,160
or four possible states two to the three is eight two to the four is 16.

68
00:05:22,200 --> 00:05:26,190
Now this is one that causes confusion in decimal 

69
00:05:26,190 --> 00:05:33,300
we don't start at one we've started zero and then we count zero one two three ignoring negative numbers

70
00:05:33,330 --> 00:05:39,840
obviously but let's assume positive integer numbers we start at zero and then we count up now in binary

71
00:05:40,080 --> 00:05:47,650
we've got 2 to the power of 0. So to two no cables as an analogy equals one.

72
00:05:47,700 --> 00:05:49,950
So we don't start with one cable.

73
00:05:49,950 --> 00:05:52,500
We start with zero cables.

74
00:05:52,500 --> 00:05:54,360
Now this is once again just an analogy.

75
00:05:54,360 --> 00:05:58,660
So if the analogy doesn't work too well for you then just stick with the math.

76
00:05:58,800 --> 00:06:01,110
Just work with a math or maths if you prefer.

77
00:06:01,500 --> 00:06:08,500
So what I need you to remember is 2 to the power of 0 is 1, 2 to the power of 1 is to 2

78
00:06:08,540 --> 00:06:12,760
2 to the power of 2 is for 4, 2 to the power 3 is 8, 2 to the power of 4 is 16.

79
00:06:12,870 --> 00:06:18,450
And if we continue 2 to the power of 5 is 32, 2 to the power of 6 is 64, 2 to the power

80
00:06:18,450 --> 00:06:27,090
of 7 is 128, 2 to the power of 8 is 256 but in an IPv4 address we've got what's called

81
00:06:27,090 --> 00:06:31,020
an octet which is eight binary values.

82
00:06:31,080 --> 00:06:34,850
So we've got eight values but we start counting at zero.

83
00:06:34,860 --> 00:06:43,080
So we've got 0,1, 2, 3, 4, 5, 6, 7. Let's formalize that by showing you a really important

84
00:06:43,080 --> 00:06:44,340
table.

85
00:06:44,340 --> 00:06:49,060
Now if you're ever going to learn a table then this is the table that I suggest that you learn.

86
00:06:49,060 --> 00:06:51,850
It's really important for the CCNA exam.

87
00:06:51,900 --> 00:06:59,720
Make sure that you know this table before you go and take your exam. Notice we have at the top here 2

88
00:06:59,750 --> 00:07:06,180
to the power of 0, 2 to the power of 1, 2 to the power of 2, 2 to the power of 3, 4, 5

89
00:07:06,330 --> 00:07:08,100
6 and 7

90
00:07:08,100 --> 00:07:17,160
Notice we're counting from 0 to 7 but that's 1, 2, 3, 4, 5, 6, 7, 8

91
00:07:17,250 --> 00:07:23,330
If we set this value to 1 in binary in decimal that equates to 1.

92
00:07:23,580 --> 00:07:27,870
If we set this value to 1 in binary it equates to 2.

93
00:07:27,930 --> 00:07:29,930
This value equates to 4.

94
00:07:30,150 --> 00:07:38,830
This equates to 8, this to 16, this to 32, this to 64 ,this to 128.

95
00:07:38,850 --> 00:07:43,560
Remember that 2 to power of 7 is 128.

96
00:07:43,560 --> 00:07:49,150
And there's our seven 2 to the power of 6 equals 64.

97
00:07:49,290 --> 00:07:53,540
Or if you like 2 to the power of 2 equals 4.

98
00:07:53,580 --> 00:07:58,920
So when this bit is set on it means 4 in decimal.

99
00:07:58,920 --> 00:08:03,330
Now in the real world, you're going to use a calculator but you need to understand the basics before

100
00:08:03,330 --> 00:08:04,860
you use calculators.

101
00:08:04,860 --> 00:08:07,710
So we're going to do a lot of this manually first.

102
00:08:07,710 --> 00:08:13,070
And when you take your CCNA exam you can't take a calculator into the exam with you.

103
00:08:13,080 --> 00:08:15,660
So you need to know how to do this in your head.

104
00:08:15,660 --> 00:08:22,040
So we're going to do it manually but again for the real world you'll use a calculator. So in this table

105
00:08:22,040 --> 00:08:24,360
we have what's called the base exponent.

106
00:08:24,380 --> 00:08:29,870
So we've got starting on the right inside side 2 to the power of 0, 2 to the power of 1, 2 to the power of 2

107
00:08:29,870 --> 00:08:33,220
2 to the power of 3 4 5 6 and 7.

108
00:08:33,440 --> 00:08:35,919
And then we've got a binary equivalent.

109
00:08:35,990 --> 00:08:40,980
So if we set this to binary 1 and then the decimal equivalent is 128.

110
00:08:41,120 --> 00:08:46,450
If I set this to binary 1 decimal equivalent is 2.

111
00:08:46,520 --> 00:08:53,710
To help you understand that let's do an example. Let's say I gave you a number of 255, 255

112
00:08:53,720 --> 00:08:58,910
if we take the decimal equivalence is equal to 128.

113
00:08:58,910 --> 00:09:01,970
In other words this bit is set on 64.

114
00:09:01,970 --> 00:09:11,600
In other words this bit is set on 32, 16, 8, 4, 2 and 1.

115
00:09:11,660 --> 00:09:18,510
In other words if I add 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 I get 255

116
00:09:18,510 --> 00:09:30,620
in decimal that is represented as this in binary. So in binary eight binary 1s equates to 255

117
00:09:31,010 --> 00:09:37,940
because this equals binary 1, this equals 128 in decimal.