GATE CS 2024 Set 1 Q18 — Combinational Circuits

The given circuit represents an AND gate with inputs $X$ and its complement $\bar{X}$ (obtained via a NOT gate). Thus, the output is given by:

Case 1: With no propagation delays
Since the signals propagate instantaneously, the inputs to the AND gate are always complementary. Therefore, $Y = X \cdot \bar{X} = 0$ at all times. This makes Option A correct and Option B incorrect.

Case 2: With propagation delays
Let the propagation delay of the NOT gate be $\tau$.

• Transition of $X$ from $0 \to 1$: Initially, $X = 0$ and $\bar{X} = 1$, so $Y = 0$. When $X$ changes to $1$, the direct input to the AND gate becomes $1$ instantly. However, due to the delay $\tau$, the output of the NOT gate remains at $1$ for a duration of $\tau$. During this transient interval, both inputs to the AND gate are $1$, causing the output $Y$ to momentarily rise to logic $1$ (a static-0 hazard). This makes Option C correct.
• Transition of $X$ from $1 \to 0$: Initially, $X = 1$ and $\bar{X} = 0$, so $Y = 0$. When $X$ changes to $0$, the direct input to the AND gate becomes $0$ instantly. The output of the NOT gate changes from $0$ to $1$ only after delay $\tau$. Since at least one input to the AND gate is always $0$ during this transition, the output $Y$ remains stable at $0$ with no transient pulse. Thus, Option D is incorrect.