Question

The inputs and outputs for different time intervals are given below the NAND gate.

\[ \begin{array}{|c|c|c|c|} \hline \text{Time} & \text{Inputs A} & \text{Inputs B} & \text{Outputs Y} \\ \hline t_1 \text{ to } t_2 & 0 & 1 & P \\ t_2 \text{ to } t_3 & 0 & 0 & Q \\ t_3 \text{ to } t_4 & 1 & 0 & R \\ t_4 \text{ to } t_5 & 1 & 1 & S \\ \hline \end{array} \]

The values taken by \(P\), \(Q\), \(R\), and \(S\) are respectively:

• A. 1, 1, 1, 0
• B. 0, 1, 0, 1
• C. 0, 1, 1, 0
• D. 1, 0, 1, 1

Hint:

NAND gate truth: output is LOW (0) only when ALL inputs are HIGH (1). For any other input combination, output is HIGH (1).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a NAND gate: Output \(= \overline{A \cdot B}\). Output is 0 only when both inputs are 1; otherwise output is 1.
Step 2: Detailed Explanation:
\(P\): \(A=0, B=1 \Rightarrow \overline{0 \cdot 1} = \overline{0} = 1\)
\(Q\): \(A=0, B=0 \Rightarrow \overline{0 \cdot 0} = \overline{0} = 1\)
\(R\): \(A=1, B=0 \Rightarrow \overline{1 \cdot 0} = \overline{0} = 1\)
\(S\): \(A=1, B=1 \Rightarrow \overline{1 \cdot 1} = \overline{1} = 0\)
Step 3: Final Answer:
\(P, Q, R, S = 1, 1, 1, 0\).