GATE 2010 CS (CS1) – Question 41

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

Find the output of the NOR-gate network shown.

Diagram for GATE 2010 CS (CS1) question 41

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

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Show answer and explanation

Correct answer: (A) $\overline{Q+R}$

Explanation

The upper pair of first-level NOR outputs combines to $\overline{\overline{P+Q}+\overline{Q+R}}=(P+Q)(Q+R)=Q+PR$. The lower branch similarly gives R+PQ. The final NOR output is the complement of Q+PR+R+PQ. Absorption reduces this to $\overline{Q+R}$, A.

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