Question

What is the Boolean expression for a two-input NAND gate?

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

Hint:

NAND gate = NOT(AND). Boolean expression: \[ Y = \overline{AB} \] It is also known as a {universal logic gate}.

Answer 1

The Correct Option is C

Concept: A NAND gate is a digital logic gate that performs the NOT operation on the output of an AND gate.
Step 1: Write the AND gate expression.} For two inputs \(A\) and \(B\), \[ Y_{AND} = AB \]
Step 2: Apply the NOT operation.} Taking the complement of the AND output, \[ Y = \overline{AB} \]
Step 3: Interpretation.} The output of a NAND gate becomes \(0\) only when both inputs are \(1\). In all other cases, the output is \(1\). Thus, the Boolean expression of a two-input NAND gate is \[ Y = \overline{AB} \]