Digital LogicFor two binary variables (taking values 0 and 1) there are 16 possible functions. The functions involve only three operations which make up Boolean algebra: AND, OR, and COMPLEMENT. They are symbolically represented as follows: These operations are like ordinary algebraic operations in that they are commutative, associative, and distributive. There is a group of useful theorems of Boolean algebra which help in developing the logic for a given operation.

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Boolean Algebra TheoremsThe applications of digital logic involve functions of the AND, OR, and NOT operations. These operations are subject to the following identities: These theorems can be used in the algebraic simplification of logic circuits which come from a straightforward application of a truth table.

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Binary Functions of Two VariablesDigital logic involves combinations of the three types of operations for two variables: AND, OR, and NOT. There are sixteen possible functions: 
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Single Variable Theorems

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TwoVariable TheoremsBesides the important DeMorgan's Theorem, the theorems below have utility in digital circuits. They have no direct counterparts in ordinary algebra.

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