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Boolean Algebra

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Boolean Algebra

Boolean Algebra, invented by mathematician George Boole (1815-1864), is a way of expressing logic in mathematical terms. In a Boolean algebra, there are several common operations, which we can express as common logical statements:

• NOT: Inverts a number
• AND: Returns the greatest lower bound
• OR: Returns the least upper bound
• XOR: Returns the difference (which bits are different)

In a Boolean algebra, there are two possible inputs, 1 and 0, and as a result:

• NOT: Returns 1 if input is 0 and 0 if input is 1.
• AND: Returns 1 only if both inputs are 1.
• OR: Returns 1 if at least one input is 1.
• XOR: Returns 1 if the inputs are different (1,0) and 0 if they are the same (0,0 or 1,1).

These simple devices (AND, OR, XOR, NOT) are known as logic gates, and a typical microprocessor has an innumerable number. Computers, at the electronic circuitry level, are composed of these gates, and do all their work in binary arithmetic.

http://www.digitalcentury.com/encyclo/update/boole.html
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