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?

The given circuit computes the Boolean function:

1. Ideal Case (No Propagation Delays):

   • In Boolean algebra, $X \cdot \overline{X} = 0$ 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 $\Delta t > 0$.

   • 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 $0 \le t < \Delta t$ due to propagation delay.

     • During this time interval $(0, \Delta t)$, 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 $t = \Delta t$ 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.