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Binary Counting

With the decimal numbering system, counting uses the numbers in the base, 0 through 9. With this system, the digits continue to increase until they reach 9. Then an additional 1 would be included with the addition of a new high-order bit. For example, similar to the way decimal 99 increments to 100 decimal, the next binary number after 11 is 100. Notice, that as the “1” position and “2” position go to 0s, an additional 1 is included in the “4” position.

The binary number system uses only two digits, 0 and 1. Because there are only two digits in the binary numbering system, the counting process is simpler than in other numbering systems. So, counting is only 0 and 1 before a new column is added. Like other numbering systems, leading 0s do not affect the value of the number. However, because we are repre-senting the status of a byte of address or data, we include these as placeholders. Table 6-8 show an example of binary counting.

Table 6-8	Binary Counting
Decimal	Binary	Decimal	Binary	Decimal	Binary
0	00000000	16	00010000	32	00100000
1	00000001	17	00010001	33	00100001
2	00000010	18	00010010	34	00100010
3	00000011	19	00010011	35	00100011

Decimal	Binary	Decimal	Binary	Decimal	Binary
4	00000100	20	00010100	36	00100100
5	00000101	21	00010101	37	00100101
6	00000110	22	00010110	38	00100110
7	00000111	23	00010111	39	00100111
8	00001000	24	00011000	40	00101000
9	00001001	25	00011001	41	00101001
10	00001010	26	00011010	42	00101010
11	00001011	27	00011011	43	00101011
12	00001100	28	00011100	44	00101100
13	00001101	29	00011101	45	00101101
14	00001110	30	00011110	46	00101110
15	00001111	31	00011111	47	00101111