1
00:00:00,000 --> 00:00:06,000
Now continuing with the analogy, imagine that you two cables

2
00:00:06,000 --> 00:00:09,000
two cables can either have no current applied

3
00:00:09,000 --> 00:00:12,000
so no current equates to 00 or for example you could have no current

4
00:00:12,000 --> 00:00:20,000
on the first cable but have current on the second cable and that equates to 01

5
00:00:20,000 --> 00:00:24,000
once again no current equals 0, current equals 1

6
00:00:24,000 --> 00:00:28,000
And continuing with that example, you could have current on the first cable

7
00:00:28,000 --> 00:00:34,000
and no current on the second cable, that gives us the value of 10

8
00:00:34,000 --> 00:00:38,000
or we could have a current on both cables, so current on cable 1

9
00:00:38,000 --> 00:00:45,000
and current on cable 2, gives us a value of 11, so in this case, we have

10
00:00:45,000 --> 00:00:51,000
2 cables but there are 4 combinations or 4 options, 00 no current on both

11
00:00:51,000 --> 00:00:59,000
01 no current on first, but current on second or 10 current no current

12
00:00:59,000 --> 00:01:03,000
or 11 which means current on both

13
00:01:03,000 --> 00:01:08,000
The reason for this is that we have 2 cables and 2 possible states

14
00:01:08,000 --> 00:01:15,000
either on or off, so 2  cables with 2 possible states gives us the value of 4

15
00:01:15,000 --> 00:01:21,000
or 2 to the power of 2 equals 4, or if you prefer 2 x 2 = 4

16
00:01:21,000 --> 00:01:27,000
So just ot summarize, in this example, we have 2 cables and 2 states per cable

17
00:01:27,000 --> 00:01:32,000
2 cables times 2 states equals 4 combinations

18
00:01:32,000 --> 00:01:37,000
thus 2 x 2 = 4 or 2 to the power of 2 equals 4

19
00:01:37,000 --> 00:01:43,000
So extending that analogy to 8 cables, the reason why we're using 8 is that

20
00:01:43,000 --> 00:01:50,000
an IPv4 Address consists of 4 octets or 4 8 bit values

21
00:01:50,000 --> 00:01:54,000
In this case, we might have no current on the first 7 cables

22
00:01:54,000 --> 00:02:03,000
and current on the last cable that gives us 7 binary 0s and a single binary 1

23
00:02:03,000 --> 00:02:08,000
we could once again go through all the various combinations as per the previous

24
00:02:08,000 --> 00:02:14,000
examples where we put current on the last cable as in this example

25
00:02:14,000 --> 00:02:19,000
or current on the second last cable and then go through all the combinations

26
00:02:19,000 --> 00:02:24,000
until we reach the situation where we had current on all the cables

27
00:02:24,000 --> 00:02:30,000
if you went through all the combinations, you would end up having

28
00:02:30,000 --> 00:02:40,000
256 combinations or 256 binary values, 2 states across 8 cables gives you 256

29
00:02:40,000 --> 00:02:44,000
Now for the sake of time we're not going to do that here but if you do

30
00:02:44,000 --> 00:02:49,000
decide to work it out, you would see that you have 256 binary combinations

31
00:02:49,000 --> 00:02:54,000
Now let's do a quick comparison between decimal and binary systems

32
00:02:54,000 --> 00:03:00,000
Decimal is based on a 10 based system where it has values from 0 to 9

33
00:03:00,000 --> 00:03:06,000
this is the numbering system used in everyday Math or Maths or Mathematics

34
00:03:06,000 --> 00:03:11,000
whichever term you prefer. Binary, however, is 2 based system

35
00:03:11,000 --> 00:03:14,000
which is the foundation of computer operations

36
00:03:14,000 --> 00:03:20,000
once again we have 2 values either 0 or 1, this is once again what we're

37
00:03:20,000 --> 00:03:23,000
going to concentrate on throughout the rest of this video

38
00:03:23,000 --> 00:03:29,000
So all examples are going to be using a combination of 0s and 1s

39
00:03:29,000 --> 00:03:34,000
Here's some basic Math examples for those of you who may have forgotten

40
00:03:34,000 --> 00:03:40,000
2 to the power of 0 equals 1, 2 to the power of 1 which in other words

41
00:03:40,000 --> 00:03:46,000
2 multiplied together 1 time in another words 2 x 1 = 2

42
00:03:46,000 --> 00:03:53,000
Now extending that, 2 to the power of 2 which is 2 x 2 = 4

43
00:03:53,000 --> 00:03:58,000
2 to the power of 3, which is 2 multiplied together 3 times

44
00:03:58,000 --> 00:04:05,000
in other words 2 x 2 x 2 = 8, 2 to the power of 4 which is once again

45
00:04:05,000 --> 00:04:09,000
2 multiplied together 4 times equals 16

46
00:04:09,000 --> 00:04:14,000
Continuing 2 to the power of 5 equals 32

47
00:04:14,000 --> 00:04:17,000
2 to the power of 6 is equals to 64

48
00:04:17,000 --> 00:04:20,000
2 to the power of 7 equals 128

49
00:04:20,000 --> 00:04:24,000
2 to the power of 8 equals 256

50
00:04:24,000 --> 00:04:29,000
So that's some basic Math, essentially 2 to the power of a value is the

51
00:04:29,000 --> 00:04:35,000
value multiplied by itself, in this case, 2 to the power of 8 is

52
00:04:35,000 --> 00:04:41,000
2 multiplied by itself 8 times which gives you 256

53
00:04:41,000 --> 00:04:46,000
Now this is kind of basic Math is really important

54
00:04:46,000 --> 00:04:49,000
when working with Binary, IP Addressing and Subnetting

55
00:04:49,000 --> 00:04:54,000
Now if you were ever going to learn a table to help you Binary and Subnetting

56
00:04:54,000 --> 00:04:59,000
then this would be it. In the real world, we typically use calculators

57
00:04:59,000 --> 00:05:02,000
but it's well worth knowing how to do this manually

58
00:05:02,000 --> 00:05:05,000
to help you with your understanding. So if you ever need to work out

59
00:05:05,000 --> 00:05:10,000
Subnetting or Binary manually, I suggest that you write down this table

60
00:05:10,000 --> 00:05:14,000
because it will make your life a lot easier when working out binary to

61
00:05:14,000 --> 00:05:20,000
decimal and decimal to binary. What you have in this table is firstly your

62
00:05:20,000 --> 00:05:26,000
base exponent, so 2 to the power of 7, 2 to the power of 6, 2 to the power of 5

63
00:05:26,000 --> 00:05:29,000
all the way down to 2 to the power of 0

64
00:05:29,000 --> 00:05:33,000
put binary 1s below that and then the decimal equivalent

65
00:05:33,000 --> 00:05:41,000
So 2 to the power of 7 equals 128, 2 to the power of 6 equals 64

66
00:05:41,000 --> 00:05:48,000
2 to the power of 5 is 32, 2 to the power of 4 is 16, 2 to the power of 3 is 8

67
00:05:48,000 --> 00:05:52,000
2 to the power of 2 is 4, 2 to the power of 1 is 2

68
00:05:52,000 --> 00:05:56,000
and lastly 2 to the power of 0 is 1

69
00:05:56,000 --> 00:06:00,000
Now these values are really important in IPv4,

70
00:06:00,000 --> 00:06:05,000
so it's well-worth remembering this table