Vol. Digital Circuits
Chapter 7 Boolean Algebra

The Exclusive-OR Function: The XOR Gate

What Is an XOR Gate?

One element conspicuously missing from the set of Boolean operations is that of Exclusive-OR, often represented as XOR.

Whereas the OR function is equivalent to Boolean addition, the AND function to Boolean multiplication, and the NOT function (inverter) to Boolean complementation, there is no direct Boolean equivalent for Exclusive-OR.

This hasn’t stopped people from developing a symbol to represent this logic gate, though:


Developing a symbol to represent this logic gate for XOR Gate.


This logic gate symbol is seldom used in Boolean expressions because the identities, laws, and rules of simplification involving addition, multiplication, and complementation do not apply to it.

However, there is a way to represent the Exclusive-OR function in terms of OR and AND, as has been shown in previous chapters: AB’ + A’B


The Exclusive-OR function in terms of OR and AND.


As a Boolean equivalency, this rule may be helpful in simplifying some Boolean expressions.

Any expression following the AB’ + A’B form (two AND gates and an OR gate) may be replaced by a single Exclusive-OR gate.