Page 10 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 1: Number Systems

Notes
Figure 1.3: Binary Counting Sequence

The binary counting sequence has an important characteristic, as shown in Figure 1.3 the units
bit (LSB) changes either from 0 to 1 or 1 to 0 with each count. The second bit (two’s position)
stays at 0 for two counts, then at 1 for two counts, then at 0 for two counts, and so on. The third
bit (fours position) stays at 0 for four counts, then at 1 for four counts, and so on. The fourth
bit (eights position) stays at 0 for eight counts, then at 1 for eight counts. If we wanted to count
further we would add more places, and this pattern would continue with 0s and 1s alternating
in groups of 2 N–1 . For example, using a fifth binary place, the fifth bit would alternate sixteen 0s,
then sixteen 1s, and so on.
As we saw for the decimal system, it is also true for the binary system that by using N-bits or
2
places we can go through 2 counts. For example, with 2-bits we can go through 2 = 4 counts
N
(00 through 11 ); with 4-bits we can go through 2 = 16 counts (0000 through 1111 ); and so on.
4
2 2 2 2
N
The last count will always be all is and is equal to 2 –1 in the decimal system. For example, using
4-bits, the last count is 11112 = V – 1= 1510.
Self Assessment
Choose the correct answer:
1. The decimal number system is composed of ..................... numerals or symbols.
(a) 8 (b) 10
(c) 11 (d) 15
2. The base of the decimal number is ..................... .
(a) 0 (b) 10
(c) 11 (d) 8

3. Binary system there are only two symbols or possible digit values, and ..................... .
(a) 1 and 2 (b) 8 and 10
(c) 0 and 1 (d) 8 and 2

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