17.2 BOOLEAN ALGEBRA
Discrete algebra with variables assigned the values of either 0 or 1, developed by George Boole, is called Boolean algebra. It is the foundation for all digital designs. A practical switch S connected between two nodes X and Y has two states. It is either open (P = 0) as shown in Fig. 17.1(a) or closed (P = 1) as shown in Fig. 17.1(b).
FIGURE 17.1 A practical switch: (a) open state; (b) closed state
TABLE 17.1 The truth table for a switch
| S.No. | P | f = P |
|---|---|---|
| 1 | 0 | 0 (switch S open) |
| 2 | 1 | 1 (switch S closed) |
TABLE 17.2 The truth table for the AND operation
Let f denote the connectivity between X and Y. Then we ...
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