Question

A logic gate circuit is shown in the figure below. The correct combination for the input \( (P, Q) \) for which the output \( T = 1 \) is:

 

• A. \( (0,0) \)
• B. \( (0,1) \)
• C. \( (1,1) \)
• D. \( (1,0) \)

Hint:

In logic gate circuits, start by analyzing each gate’s behavior, then apply the inputs to determine the output step by step.

Answer 1

The Correct Option is A

The given circuit consists of two NOT gates followed by an AND gate. Let's analyze the circuit step-by-step:

Step 1: Understand the behavior of the NOT gates.
The first NOT gate inverts the input \( P \).
The second NOT gate inverts the input \( Q \).

Step 2: Determine the outputs of the NOT gates.
If \( P = 0 \), after passing through the first NOT gate, the output will be \( \overline{P} = 1 \).
If \( Q = 0 \), after passing through the second NOT gate, the output will be \( \overline{Q} = 1 \).

Step 3: Understand the operation of the AND gate.
The output of the AND gate is 1 if both inputs to the gate are 1. Hence, the output of the AND gate is:
\[ T = \overline{P} \cdot \overline{Q} \]

Step 4: Check the outputs for all combinations of \( P \) and \( Q \):

• If \( P = 0 \) and \( Q = 0 \), then \( \overline{P} = 1 \) and \( \overline{Q} = 1 \), so the output is \( 1 \cdot 1 = 1 \). ✅
• If \( P = 0 \) and \( Q = 1 \), then \( \overline{P} = 1 \) and \( \overline{Q} = 0 \), so the output is \( 1 \cdot 0 = 0 \). ❌
• If \( P = 1 \) and \( Q = 0 \), then \( \overline{P} = 0 \) and \( \overline{Q} = 1 \), so the output is \( 0 \cdot 1 = 0 \). ❌
• If \( P = 1 \) and \( Q = 1 \), then \( \overline{P} = 0 \) and \( \overline{Q} = 0 \), so the output is \( 0 \cdot 0 = 0 \). ❌

Conclusion:
The correct combination for which \( T = 1 \) is \( (P, Q) = (0, 0) \).