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Revision as of 04:49, December 11, 2007
, 04:49, December 11, 2007→Three Basic Operations
==Three Basic Operations==
==Three Basic Operations==
The three basic operations of boolean algebra are AND ([[multiplication]]), OR ([[addition]]), and NOT. From these functions, the other functions of boolean algebra can be derived.
The three basic operations of boolean algebra are AND ([[multiplication]]), OR ([[addition]]), and NOT. See the table below for a numerical description. From these functions, the other functions of boolean algebra can be derived.
{| class="wikitable" align="left"
{| class="wikitable" align="left"
| 1 || 1 || 1 || 1 || 0 || 1
| 1 || 1 || 1 || 1 || 0 || 1
|}
|}
AND (shown to the right) is the boolean equivalent of multiplication.
===AND===
AND is the boolean equivalent of multiplication. In words, the AND function states: "If A AND B are true then C is true". Numerically, the product of two numbers can only be non-zero if both numbers are non-zero. The AND function is commutative, so it works no matter what order the values are in. For example, A • B = B • A, and A • (B • C) = (A • B) • C.
Just as in traditional [[algebra]], [[exponent]]s can be represented as a series of multiplications in boolean algebra, but the results are different. A<sup>n</sup> can be represented as the value A multiplied n times, or A•A•A•A... = C. Boolean multiplication returns a "true" (or a 1) if all values are "true" (or 1), but in this case, all values are always the same. So if A = 0, C = 0, and if A = 1, C = 1. This means that A<sup>n</sup> simply reduces to A!
{{clear}}
{{clear}}
===test===
===test===