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Computing (FOLDOC) dictionary

two-valued logic

logic (Commonly known as "Boolean algebra") A mathematical

system concerning the two truth values, TRUE and FALSE and

the cornerstones of logic and is also fundamental in the

design of digital electronics and programming languages.

The term "Boolean" is used here with its common meaning -

two-valued, though strictly Boolean algebra is more general

than this.

Boolean functions are usually represented by truth tables

where "0" represents "false" and "1" represents "true". E.g.:

A | B | A AND B

--+---+--------

0 | 0 | 0

0 | 1 | 0

1 | 0 | 0

1 | 1 | 1

This can be given more compactly using "x" to mean "don't

care" (either true or false):

A | B | A AND B

--+---+--------

0 | x | 0

x | 0 | 0

1 | 1 | 1

Similarly:

A | NOT A A | B | A OR B

--+------ --+---+--------

0 | 1 0 | 0 | 0

1 | 0 x | 1 | 1

1 | x | 1

more than two inputs can be constructed using combinations of

AND, OR, and NOT. AND and OR can be constructed from each

other using DeMorgan's Theorem:

A OR B = NOT ((NOT A) AND (NOT B))

A AND B = NOT ((NOT A) OR (NOT B))