Digital Logic · Boolean Algebra and Minimization
Official IIT answer key · IIT Guwahati · Audited Aug 2026
GATE CSE 2025 Set 1 Q42 · MCQ · 2 marks
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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 four variable Boolean function in sum-of-product form F(b3, b2, b1, b0) = (0, 2, 4, 8, 10, 11, 12). where the value of the function is computed by considering b3 b2 b1 b0 as a 4-bit binary number, where b3 denotes the most significant bit and b0 denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for F?
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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.
