For F=P+QR, consider S1 F=(4,5,6); S2 F=(0,1,2,3,7); S3 F=(4,5,6); S4 F=(0,1,2,3,7). Which truth-value pattern applies?

S1 true,S2 false,S3 false,S4 true

S1 false,S2 false,S3 true,S4 true

S1 true,S2 true,S3 false,S4 false

GATE 2015 CS (CS3) – Question 40

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

For $F=P\prime+QR$, consider S1 $F=\Sigma(4,5,6)$; S2 $F=\Sigma(0,1,2,3,7)$; S3 $F=\Pi(4,5,6)$; S4 $F=\Pi(0,1,2,3,7)$. Which truth-value pattern applies?

S1 false,S2 true,S3 true,S4 false
S1 true,S2 false,S3 false,S4 true
S1 false,S2 false,S3 true,S4 true
S1 true,S2 true,S3 false,S4 false

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Correct answer: (A) S1 false,S2 true,S3 true,S4 false

Explanation

When P=0, F is one for minterms zero through three. With P=1 it is one only when Q=R=1, minterm seven. Thus the sum of minterms is {0,1,2,3,7}, and the product of zero-valued maxterms is {4,5,6}. Hence only S2,S3 are true, A.

GATE 2015 CS (CS3) – Question 40

Explanation

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