With XOR denoted and binary constants 1,0, simplify F(P,Q)=((1 P)(P Q))((P Q)(Q0)).

GATE 2014 CS (CS3) – Question 65

Digital Logic · Boolean Algebra and Minimization · 2 marks · Multiple choice

With XOR denoted $\oplus$ and binary constants 1,0, simplify $F(P,Q)=((1\oplus P)\oplus(P\oplus Q))\oplus((P\oplus Q)\oplus(Q\oplus0))$.

$P+Q$
$\overline{P+Q}$
$P\oplus Q$
$\overline{P\oplus Q}$

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Correct answer: (D) $\overline{P\oplus Q}$

Explanation

XORis associative and commutative, withx⊕x=0. Expanding all groups cancels pairs, leaving1⊕P⊕Q. XORwith1complements its argument, so the result is **complement(P⊕Q),D**, theXNORfunction. The parentheses do not change this parity calculation.