Question

In Boolean algebra the output \( C \) and the inputs \( A \) and \( B \) are related as \( C = \overline{A \cdot B} \). The logic gate corresponding to this equation is

• A. NOT
• B. AND
• C. OR
• D. NAND

Hint:

In Boolean algebra, \( \overline{A \cdot B} \) represents the NAND operation, which is the negation of the AND operation.

Answer 1

The Correct Option is D

Step 1: Understanding the equation.
The given equation is \( C = \overline{A \cdot B} \), which is the negation of the AND operation between \( A \) and \( B \). Step 2: Identify the corresponding logic gate.
The logic gate that performs the negation of the AND operation is the NAND gate. The NAND gate outputs 1 when at least one of its inputs is 0, and it outputs 0 only when both inputs are 1. Step 3: Conclusion.
Thus, the logic gate corresponding to \( C = \overline{A \cdot B} \) is the NAND gate, which corresponds to option (D).