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In the binary system, an IP address is represented as a sequence of 32 digits. This sequence of digits can be divided into four fields, each of which is called an octet or byte. Each octet consists of eight bits. One bit has the value 0 or 1. Thus, an IP address consists of 4 bytes, which is a total of 32 bits. An example of an octet in binary notation is 11011001, and an example of an IP address in binary notation is 00001010 11011001 01111011 00000111. The decimal notation of this octet and IP address is 217 and 10.217.123.7, respectively.
Decimal Notation
In decimal notation, or base 10 notation, calculate the value of a number as follows: Starting with the digit furthest to the right, multiply each digit by increasing powers of 10 (starting with 100). Then add these values to get the number. For example, the calculation for the number 217 is:
7*100 = 7*1 = 7
1*101 = 1*10 = 10
2*102 = 2*100 = 200
200+10+7 = 217
Binary notation
To calculate the decimal value of a number in binary notation, use a similar procedure. In this case, replace the base 10 with the base 2. Multiply each digit in the representation by powers of 2 instead of powers of 10. For example, for the number 11011001, starting with the digit furthest to the right gives the calculation:
1*20 = 1*1 = 1
0*21 = 0*2 = 0
0*22 = 0*4 = 0
1*23 = 1*8 = 8
1*24 = 1*16 = 16
0*25 = 0*32 = 0
1*26 = 1*64 = 64
1*27 = 1*128 = 128
128+64+0+16+8+0+0+1 = 217
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