Question

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? \begin{center} \includegraphics[width=8cm]{28.png} \end{center}

• 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

Hint:

Propagation delays in logic gates can lead to transient outputs. Always consider the gate timing when analyzing circuit behavior during transitions.

Answer 1

The Correct Option is A

Step 1: Analyze the circuit without propagation delays.
The circuit includes an AND gate and a NOT gate. The input to the AND gate is \( X \) and the output of the NOT gate (i.e., \( \neg X \)).
The AND gate has two inputs: \( X \) and \( \neg X \). For any value of \( X \): \[ Y = X \land \neg X. \] Since \( X \land \neg X = 0 \) for all values of \( X \), the output \( Y \) is always logic Zero without propagation delays. Thus, Option (1) is TRUE, and Option (2) is FALSE. Step 2: Analyze the circuit with propagation delays. When \( X \) transitions from logic Zero to logic One:
1. The NOT gate takes some time to invert the signal from \( X \) to \( \neg X \).
2. During this propagation delay, both inputs of the AND gate could temporarily be logic One.
This causes a transient logic One at \( Y \). Thus, Option (3) is TRUE.
When \( X \) transitions from logic One to logic Zero, the NOT gate's propagation delay does not lead to a transient logic Zero at \( Y \), because the AND gate will have at least one input at logic Zero. Thus, Option (4) is FALSE. Final Answer: \[ \boxed{\text{(1) and (3)}} \]