Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT? A) With no propagation delays, the output Y is always logic Zero B) With no propagation delays, the output Y is always logic One C) With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One D) With propagation delays, the output Y can have a transient logic Zero after X transitions from logic One to logic Zero

Official answer: A) With no propagation delays, the output Y is always logic Zero; C) With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One. Explanation: The given circuit computes the Boolean function: Y = X X 1. Ideal Case (No Propagation Delays): - In Boolean algebra, X X = 0 for all values of X. - Hence, with no propagation delays, the output Y is always logic Zero. *(Statement A is correct, Statement B is incorrect)* 2. Real Case (With Propagation Delays): - Let the NOT gate have a propagation delay of t > 0. - Consider X transitioning from logic Zero to logic One at t = 0: - The direct input to the AND gate becomes 1 at t = 0. - The output of the NOT gate was 1 (for X = 0) and remains 1 for 0 t < t due to propagation delay. - During this time interval (0, t), both inputs to the AND gate are 1. - Consequently, the output Y produces a transient high pulse (logic One) known as a static-0 hazard / glitch. *(Statement C is correct)* - Consider X transitioning from logic One to logic Zero at t = 0: - The direct input to the AND gate immediately drops to 0 at t = 0. - The output of the NOT gate remains 0 until t = t before changing to 1. - The inputs to the AND gate are (0, 0) initially and then (0, 1), so the output Y remains steady at logic Zero with no glitch. *(Statement D is incorrect)* Therefore, the correct statements are A and C.

A) With no propagation delays, the output Y is always logic Zero

B) With no propagation delays, the output Y is always logic One

C) With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One

D) With propagation delays, the output Y can have a transient logic Zero after X transitions from logic One to logic Zero

Digital Logic · Boolean Algebra and Minimization

Official IIT answer key · IISc Bangalore · Audited Aug 2026

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GATE CSE 2024 Set 1 Q28 · MSQ · 1 mark

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Select one or more options

Key concept

Boolean Algebra and Minimization

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Examiner trap & misconception

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How GATE tests Boolean Algebra and Minimization

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.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Digital Logic · Boolean Algebra and Minimization

Official IIT answer key · IISc Bangalore · Audited Aug 2026

Take topic test

GATE CSE 2024 Set 1 Q28 · MSQ · 1 mark

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Select one or more options

Key concept

Boolean Algebra and Minimization

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Boolean Algebra and Minimization

Full Boolean Algebra and Minimization guide →

More on Boolean Algebra and Minimization

All 36 questions on Boolean Algebra and Minimization →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Step-by-step verified solution

Check you can still solve Boolean Algebra and Minimization under a clock

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Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

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Check you can still solve Boolean Algebra and Minimization under a clock

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More on Boolean Algebra and Minimization

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Step-by-step verified solution

Check you can still solve Boolean Algebra and Minimization under a clock

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Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Step-by-step verified solution

Check you can still solve Boolean Algebra and Minimization under a clock

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More on Boolean Algebra and Minimization

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