GATE CS 2024 Set 1 Q.28: Combinational Circuits

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?

Combinational circuit where input X feeds directly into the top input of a 2-input AND gate and also passes through a NOT gate into the bottom input of the AND gate to produce output Y.

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

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

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

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

Official answer and solution

Official answer: A and C
From: Official GATE 2024 answer key

Solution

Analyze the steady-state Boolean expression $Y = X \cdot \overline{X}$ and the transient static-0 hazard when $X$ switches from $0$ to $1$ with a non-zero NOT gate delay.

(A) is CORRECT and (B) is FALSE: With zero propagation delay, the inputs to the AND gate are $X$ and $\overline{X}$ at every instant, so $Y = X \cdot \overline{X} = 0$ always.
(C) is CORRECT: Suppose the NOT gate has a positive propagation delay $\tau_{\text{NOT}} > 0$ . Initially, when $X = 0$ , the upper input to the AND gate is $0$ and the NOT gate output (lower input to the AND gate) is $1$ , so $Y = 0$ . When $X$ transitions from $0 \rightarrow 1$ , the upper input of the AND gate becomes $1$ immediately, while the output of the NOT gate remains $1$ for $\tau_{\text{NOT}}$ before falling to $0$ . During that window, both inputs to the AND gate are $1$ , so $Y$ can produce a transient logic One pulse (a static-0 hazard).
(D) is FALSE: Since the steady-state value of $Y$ is already logic Zero (and when $X$ transitions $1 \rightarrow 0$ , the upper input becomes $0$ immediately while the NOT output is still $0$ ), there is no transient logic Zero.

Final answer

Options (A), (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2024 Computer Science and Information Technology - Set 1 (CS1)
Question: 28 of 65
Section: Computer Science and Information Technology

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