Changes

The terms "boolean algebra" and "boolean logic" are used interchangeably.  The words are not capitalized (except at the beginning of a sentence, of course) even though they are named after a person.

The terms "boolean algebra" and "boolean logic" are used interchangeably.  The words are not capitalized (except at the beginning of a sentence, of course) even though they are named after a person.

==Boolean Algebra and Computers==

==Boolean Algebra and Computer Hardware==

The thing that elevates boolean algebra from a somewhat obscure branch of mathematics to one of the driving forces of modern society is that it is the basis for computers.  Computers do everything in boolean logic.  All numbers are represented internally in [[binary]] (base 2) notation, with digits ("bits") 1 and 0, corresponding to "true" and "false", respectively.  Computers are then designed in terms of boolean algebra equations.  For example, addition is performed by 32 copies of these equations:

The thing that elevates boolean algebra from a somewhat obscure branch of mathematics to one of the driving forces of modern society is that it is the basis for computers.  Computers do everything in boolean logic.  All numbers are represented internally in [[binary]] (base 2) notation, with digits ("bits") 1 and 0, corresponding to "true" and "false", respectively.  Computers are then designed in terms of boolean algebra equations.  For example, addition is performed by 32 copies of these equations:

  S = (A•B•C) + (A•B'•C') + (A'•B•C') + (A'•B'•C)

  S = (A•B•C) + (A•B'•C') + (A'•B•C') + (A'•B'•C)

XOR (or "exclusive OR") gives a 1 ("true") if either of its inputs are 1, but not both. Symbolically this can be broken down into its basic operations by the expression: A XOR B = A'B + B'A.

XOR (or "exclusive OR") gives a 1 ("true") if either of its inputs are 1, but not both. Symbolically this can be broken down into its basic operations by the expression: A XOR B = A'B + B'A.

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[[Category:Mathematics]]

[[Category:Mathematics]]

[[Category:Electronics]]

[[Category:Electronics]]