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Digital Logic · Boolean Algebra and Minimization
Official IIT answer key · IIT Kharagpur · Audited Aug 2026
GATE CSE 2014 Set 3 Q7 · MCQ · 1 mark
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Topic notes
Boolean algebra and minimization in GATE CS tests algebraic identities, canonical form transformations, K-map minimization (SOP/POS with and without don't-cares), functional completeness, and the structural properties of logic operators like XOR, XNOR, and majority functions. Early years primarily featured 1-mark or 2-mark MCQs focusing on single-step simplification or finding the minimal expression. Recent years (2021–2026) show a marked shift towards multi-select questions (MSQs) testing multiple valid minimal forms, set-theoretic minterm algebra across interconnected logic gates, and deep property verification of custom or majority Boolean functions.
Full Boolean Algebra and Minimization guide →Consider the following minterm expression for F: F (P, Q, R, S) = 0, 2, 5, 7, 8, 10, 13, 15 The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-products form for F is
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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.