Exclusive-OR Function (XOR)

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One element conspicuously missing from the set of Boolean operations is that of Exclusive-OR.

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 it, though:

XOR Gate

Exclusive-OR Function

This 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.

Equivalent XOR Gate

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

Exclusive-OR Equivalent Circuit

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.

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Previous: Boolean Circuit Simplification Examples
Next: Boolean Algebraic Properties

Exclusive-OR Function (XOR)

 
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