Question

In the case of NAND gate, if A and B are inputs and Y is the output then

• A. \(Y = \overline{A+B}\)
• B. \(Y = A\cdot B\)
• C. \(Y = \overline{A\cdot B}\)
• D. \(Y = A+B\)

Hint:

NAND means NOT-AND, so put a bar over A times B.

Answer 1

The Correct Option is C

Step 1: Name tells the function:
NAND means NOT plus AND. So first AND the inputs, then complement the result.

Step 2: Output rule:
The output is 0 only when $A=1$ and $B=1$. In every other case it is 1. Written algebraically this is $Y=\overline{AB}$. By De Morgan's law it also equals $\bar A + \bar B$.

Step 3: Compare with the options:
(A) $\overline{A+B}$ is NOR, (B) $AB$ is AND and (D) $A+B$ is OR. The NAND expression is option (C).

Final Answer:
Option (C). \[ \boxed{Y=\overline{A\cdot B}} \]