Pulse and Digital Circuits

17.4 THEOREMS

Now let us consider the theorems that help in simplifying Boolean functions.

1. Idempotency TheoremThe idempotency theorem states that if P is a logical or Boolean variable such that P can take values ‘0’ or ‘1’ then P + P = P. This can be verified from the truth table given in Table 17.8. The dual of the idempotency theorem states that if P is a logical or Boolean variable such that P can take values ‘0’ or ‘1’ then P. P = P. This can be verified from the truth table given in Table 17.9.
   

   FIGURE 17.8 The realization of f = PQ + using ...