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GATE 2024 CS (CS1) – Question 28

Digital Logic · Combinational Circuits · 1 mark · Multiple select

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. The circuit feeds X directly to one AND input and NOT(X) to the other AND input, output Y. Which of the following statements about the circuit is/are CORRECT?

Diagram for GATE 2024 CS (CS1) question 28
  1. With no propagation delays, the output $Y$ is always logic Zero
  2. With no propagation delays, the output $Y$ is always logic One
  3. With propagation delays, the output $Y$ can have a transient logic One after $X$ transitions from logic Zero to logic One
  4. With propagation delays, the output $Y$ can have a transient logic Zero after $X$ transitions from logic One to logic Zero

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Show answer and explanation

Correct 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

Y = X·X' = 0 with no delays. When X rises 0→1, the direct input rises before the delayed NOT output falls, giving a brief 1 (static-0 hazard). A 1→0 transition cannot produce a transient 1 or a transient 0 since Y is already 0.