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:
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
Exclusive-OR 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 Exclusive-OR gate. |