Question

Write the Boolean expression for Exclusive-OR (XOR) gate.

Hint:

XOR output is true for odd number of true inputs; use \( \overline{A}B + A\overline{B} \) for two inputs.

Answer 1

The Exclusive-OR (XOR) gate outputs true when exactly one input is true. For inputs \( A \) and \( B \), the Boolean expression is: \[ Y = A \oplus B = \overline{A}B + A\overline{B}. \] This can be derived from the truth table: \( Y = 1 \) when \( A = 1, B = 0 \) or \( A = 0, B = 1 \).
Answer: \( Y = \overline{A}B + A\overline{B} \).