Question

The Boolean expression for X-OR gate C = `(A oplus B)` is equivalent to ______.

Options

• `(bar A * B) + (A + bar B)`

• `A + (bar A * bar B)`

• `(A * B) + bar B`

• `(A * B) + (bar A * bar B)`

Answer 1

The Boolean expression for X-OR gate C = `(A oplus B)` is equivalent to `bbunderline((bar A * B) + (A + bar B))`.

Explanation:

An X-OR gate produces a HIGH output (1) only when its two inputs are different (one is 0, the other is 1).

A	B	Output (C)
0	0	0
0	1	1 (This case is `bar A * B`)
1	0	1 (This cse is `A * bar B`)
1	1	0

By summing the “1” outputs (Sum of Products), we get:

C = `(bar A * B) + (A * vec B)`