Find the minterm expansion of f(P,Q,R)=PQ+Q R+P R.

GATE 2010 CS (CS1) – Question 16

Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple choice

Find the minterm expansion of $f(P,Q,R)=PQ+Q\bar R+P\bar R$.

$m_2+m_4+m_6+m_7$
$m_0+m_1+m_3+m_5$
$m_0+m_1+m_6+m_7$
$m_2+m_3+m_4+m_5$

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Correct answer: (A) $m_2+m_4+m_6+m_7$

Explanation

PQ contributes binary 110 and 111, minterms six and seven. QR̄ contributes 010 and 110, while PR̄ contributes 100 and 110. Their union is {2,4,6,7}, giving A, with P as the most significant minterm bit.

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