Explain the working of an XOR gate with its truth table and Boolean expression.

The XOR (Exclusive OR) gate works by outputting true (1) when the number of true inputs is odd. For a 2-input XOR gate, the output is 1 only if the inputs are different, and 0 if they are the same. The Boolean expression for a 2-input XOR gate is:

A⊕B=A′B+AB′

This expression means that the output is true when A is 0 and B is 1, or A is 1 and B is 0. The truth table for a 2-input XOR gate is as follows:

A B A ⊕ B
0 0 0
0 1 1
1 0 1
1 1 0

The XOR gate is widely used in digital systems, particularly in error detection and correction schemes, as well as in arithmetic circuits like adders.

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