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Pulse and Digital Circuits by Manmadha Rao G., Rama Sudha K., Venkata Rao K.

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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 + PR using switches

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

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