Boolean Algebra
In 1849, George Boole published a scheme for the algebraic description of processes involved in logical thought and reasoning, known as Boolean algebra.
Boolean Algebra poses a set of rules used to simplify the given logic expression without changing its functionality.
Axioms of Boolean Algebra
Single-Variable Theorems
If is a variable in , then the following theorems hold:
Principle of Duality
Given a logic expression, its dual is obtained by replacing all + operators with · operators, and vice versa, and by replacing all 0s with 1s, and vice versa.
The dual of any true statement (axiom or theorem) in Boolean algebra is also a true statement. This is based on De Morgan’s Laws (DML).
title: Why duality?
Duality implies that at least two different ways exist to express every logic function with Boolean algebra. Often, one expression leads to a simpler physical implementation than the other and is thus preferable.Two- and Three-Variable Properties
If x, y, and z are the variables in , then the following properties hold:
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