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Binary Numbering System

In the binary numbering system, the radix is 2. Therefore, each position represents increas-ing powers of 2. In 8-bit binary numbers, the positions represent the quantities shown in Table 6-1.

Table 6-1	Binary Positional Values
Powers of 2	27	26	25	24	23	22	21	20
Decimal Value	128	64	32	16	8	4	2	1

The base 2 numbering system has only two digits: 0 and 1. When a byte is interpreted as a decimal number, the quantity that position represents is added to the total if the digit is a 1, and 0 is added if the digit is a 0.

A 1 in each position means that the value for that position is added to the total. Table 6-2 shows the values of each position with a 1 in the position.

Table 6-2	Binary Positional Notation with Digit of 1
Decimal Value		128	64	32	16	8	4	2	1
Binary Digit		1	1	1	1	1	1	1	1
Position Value		128	64	32	16	8	4	2	1

The value of each position is added to determine the total value of the number. As in Table 6-1, when there is a 1 in each position of an octet, the total is 255, as follows:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255