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Line 78: − ==Boolean Algebra and Computer Programming==+ − The operations of boolean logic are extremely important in computer software. Modern computer languages usually have some kind of "boolean" data type. For example, in the C++ language, it is called "bool".
Explained computers better
==Boolean Algebra and Computer Hardware==
==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. Boolean logic is implemented in electrical circuitry by means of gates (built from many [[CMOS]] and [[nMOS]] [[transistor]]s wired together) representing the basic AND, NOT, and OR operators. These gates are then wired together to create computer chips. Therefore, everything a computer does must be represented 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; and each letter is represented by a [[ASCII|binary code]].
Computation is then done by boolean algebra operations. For example, addition is performed by performing this function on each [[bit]]:
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)
D = (A•B) + (A•C) + (B•C)
D = (A•B) + (A•C) + (B•C)
A modern computer processing chip has tens of millions of transistors, all calculating boolean operations.
A modern computer processing chip has tens of millions of transistors, all calculating boolean operations.
===Computer Programming===
The operations of boolean logic are also extremely important in computer software. Modern computer languages usually have some kind of "boolean" data type. For example, in the C++ language, it is called "bool".
==Three Basic Operations==
==Three Basic Operations==
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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