7.7. The ExclusiveOR functionOne element conspicuously missing from the set of Boolean operations is that of ExclusiveOR. 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 ExclusiveOR. This hasn't stopped people from developing a symbol to represent it, though: 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. However, there is a way to represent the ExclusiveOR function in terms of OR and AND, as has been shown in previous chapters: AB' + A'B 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 ExclusiveOR gate.
