Let ⊕ denote XOR, and 1 and 0 the binary constants. F(P, Q) = ((1 ⊕ P) ⊕ (P ⊕ Q)) ⊕ ((P ⊕ Q) ⊕ (Q ⊕ 0)). Which of the following is equivalent to F?
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Correct answer: D. (P ⊕ Q)′
Explanation
(1 ⊕ P) ⊕ (P ⊕ Q) = 1 ⊕ Q, since P ⊕ P = 0. (P ⊕ Q) ⊕ (Q ⊕ 0) = P. So F = 1 ⊕ Q ⊕ P = (P ⊕ Q)′, i.e. XNOR.
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