Question

Two inputs A and B of NAND gate have 0 output, if:

• A. \( \text{A is 0} \)
• B. \( \text{B is 0} \)
• C. \( \text{Both are zero} \)
• D. \( \text{Both are 1} \)

Hint:

A NAND gate's output is 0 only when all its inputs are 1. For all other input combinations, the output is 1. This is the opposite of an AND gate, which outputs 1 only when all inputs are 1.

Answer 1

The Correct Option is D

Step 1: Understand the behavior of a NAND gate. A NAND gate performs the logical NOT operation on the output of an AND gate. The expression for a NAND gate is \( \text{Output} = \overline{A \cdot B} \) (NOT (A AND B)). Step 2: Recall the truth table for an AND gate: \begin{itemize} \item A=0, B=0 \(\rightarrow\) A AND B = 0 \item A=0, B=1 \(\rightarrow\) A AND B = 0 \item A=1, B=0 \(\rightarrow\) A AND B = 0 \item A=1, B=1 \(\rightarrow\) A AND B = 1 \end{itemize} Step 3: Determine the output of the NAND gate by inverting the output of the AND gate: \begin{itemize} \item A=0, B=0 \(\rightarrow\) NAND Output = NOT(0) = 1 \item A=0, B=1 \(\rightarrow\) NAND Output = NOT(0) = 1 \item A=1, B=0 \(\rightarrow\) NAND Output = NOT(0) = 1 \item A=1, B=1 \(\rightarrow\) NAND Output = NOT(1) = 0 \end{itemize} Step 4: Identify the condition where the NAND gate output is 0. From the truth table in Step 3, the output is 0 only when both inputs A and B are 1. Step 5: Compare this condition with the given options. Option (d) "Both are 1" matches the condition for a 0 output.