GATE | GATE CS 2010 | Question 6

The minterm expansion of f(P, Q, R) = PQ + QR’ + PR’ is
(A) m2 + m4 + m6 + m7
(B) m0 + m1 + m3 + m5
(C) m0 + m1 + m6 + m7
(D) m2 + m3 + m4 + m5

Answer: (A)
Explanation: K-map,

= PQ + QR’ + PR’ 
= PQ(R+R’) + (P+P’)QR’ + P(Q+Q’)R’
= PQR + PQR’ +PQR’ +P’QR’ + PQR’ + PQ’R’ 
= PQR(m7) + PQR'(m6)+P’QR'(m2) +PQ’R'(m4) 
= m2 + m4 + m6 + m7 

Option (A) is correct.
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