Which binary operation does an XOR gate perform?

The XOR gate, or Exclusive OR gate, performs a specific binary operation defined as follows: it outputs true (or high) when the number of true inputs is odd. In a two-input XOR gate, this means that the output will be true if one and only one of the inputs is true. If both inputs are false or both are true, the output will be false (or low).

For instance, if you have two inputs, A and B, the XOR output can be summarized in a truth table:

• If A = 0 and B = 0, then Output = 0

• If A = 0 and B = 1, then Output = 1

• If A = 1 and B = 0, then Output = 1

• If A = 1 and B = 1, then Output = 0

This behavior highlights why it is termed "exclusive," as it only produces a true output when exactly one of its inputs is true.

The other operations listed, such as AND, OR, and NAND, do not reflect this exclusive nature of the XOR operation. The AND operation requires both inputs to be true for a true output, the OR operation requires at least one of the inputs