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Line 18: − + + − {{clear}} + − + + + − + − + − + − + − − '''Boolean [[algebra]]''' is a [[mathematics|mathematical]] system which is particularly important for [[computers]]. It consists of three logical statements AND, OR, and NOT operators. Each of the three operators corresponds to an algebraic operation. AND corresponds to [[multiplication]], OR corresponds to [[division]], NOT does not really have an algebraic equivalent. It has corallary terms such as NAND (NOT AND), NOR (NOT OR), and OT. − − − − − − {| class="wikitable" align="left" − |- − ! A !! B !! C − |- − | 0 || 0 || 0 − |- − | 0 || 1 || 0 − |- − | 1 || 0 || 0 − |- − | 1 || 1 || 1 − |} − {| class="wikitable" − |- − ! A !! B !! C − |- − | 0 || 0 || 0 − |- − | 0 || 1 || 0 − |- − | 1 || 0 || 0 − |- − | 1 || 1 || 1 − |} − − − {| border="1" − | α − | align="center" | cell2 − {| border="2" style="background-color:#ABCDEF;" − | NESTED − |- − | TABLE − |} − | valign="bottom" | the original table again − |}
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Revision as of 04:55, December 11, 2007
, 04:55, December 11, 2007→Three Basic Operations
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===AND===
===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.
AND is the boolean equivalent of multiplication. The product of two numbers are be non-zero if both numbers are non-zero. In words, the AND function states: "If A AND B are true then C is true". The AND function is commutative, so it results in the same answer 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!
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!
===OR===
===NOT===
===test===
===Order of Operations===
==Derived Functions==
===NAND and NOR===
===XOR===
<nowiki>
[[Category:Mathematics]]
[[Category:Electronics]]</nowiki>
[[category:mathematics]]