Consider a Boolean function F with the following minterm expression: F(P, Q, R, S) = m(1, 2, 3, 4, 5, 7, 10, 12, 13, 14) Which of the following options is/are the minimal sum-of-products expression(s) of F?

GATE CSE 2026 Session 1 Q48: Minimal SOP forms of Σm(1,2,3,4,5,7,10,12,13,14)

Digital Logic
2 marks
MSQ
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Consider a Boolean function F with the following minterm expression:

$F(P, Q, R, S) = \sum m(1, 2, 3, 4, 5, 7, 10, 12, 13, 14)$

Which of the following options is/are the minimal sum-of-products expression(s) of F?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, D (official GATE 2026 final answer key)

Concept used: K-map minimisation: after essential prime implicants, several equal-cost covers may remain.

First step: $\overline{P}S$ and $Q\overline{R}$ are essential; the minterms left are 2, 10 and 14, and each option must cover all three with two terms.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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GATE CSE 2026 Session 1 Q48: Minimal SOP forms of Σm(1,2,3,4,5,7,10,12,13,14)

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