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if we're consolidating pages, then boolean logic is also pretty redundant with this one
'''Boolean algebra''' or '''[[boolean logic]]''' is the formal mathematical discipline that deals with "truth values"—"true" or "false". Its fundamental operations are "and", "or" and "not". One can write "propositions" (equations) of boolean algebra, such as
'''Boolean algebra''' or '''boolean logic''' is the formal mathematical discipline that deals with "truth values"—"true" or "false". Its fundamental operations are "and", "or" and "not". One can write "propositions" (equations) of boolean algebra, such as
P = (Q+R)•(T')
P = (Q+R)•(T')
and manipulate them the way one would manipulate ordinary algebraic equations.
and manipulate them the way one would manipulate ordinary algebraic equations.
==Three Basic Operations==
==Three Basic Operations==
The three basic operations of boolean algebra are AND (analogous to [[multiplication]]), OR (analogous to [[addition]]), and NOT. See the table below for a numerical description. From these functions, the other functions of boolean algebra can be derived. In the following descriptions, we will use the 1-and-0 notation rather than the true-and-false notation.
The three basic operations of boolean algebra are AND (analogous to [[multiplication]]), OR (analogous to [[addition]]), and NOT (analogous to [[inversion]]). See the tables below for a numerical and pictorial descriptions. From these functions, the other functions of boolean algebra can be derived. In the following descriptions, we will use the 1-and-0 notation rather than the true-and-false notation.
{| class="wikitable" align="left"
{| class="wikitable" align="center"
! colspan=3 | AND: A•B=C !! !! colspan=3 | OR: A+B=C !! !! colspan=2 | NOT A'=B
! colspan=10 | Truth Table for the Operators
|- alight="left"
! colspan=3 | AND: A•B=C || || colspan=3 | OR: A+B=C || || colspan=2 | NOT A'=B
|- align="center"
|- align="center"
| '''A''' || '''B''' || '''C''' || rowspan=5 | || '''A''' || '''B''' || '''C''' || rowspan=5 | || '''A''' || '''B'''
| '''A''' || '''B''' || '''C''' || rowspan=5 | || '''A''' || '''B''' || '''C''' || rowspan=5 | || '''A''' || '''B'''
| 1 || 1 || 1 || 1 || 0 || 1
| 1 || 1 || 1 || 1 || 0 || 1
|}
|}
===AND===
===AND===
[[Image:VennAnd1.gif|right|250px|thumb|Pictorial despcription of AND]]
AND is the boolean equivalent of multiplication. The product of two numbers are 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.
AND is the boolean equivalent of multiplication. The product of two numbers are 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.
{{clear}}
===OR===
===OR===
[[Image:VennOr1.gif|right|250px|thumb|Pictorial description of OR]]
OR is the boolean equivalent of addition. The sum of two positive numbers is non-zero if either number is non-zero. In words, the OR function states: "If A OR B is true then C is true". Like AND, the OR function is commutative.
OR is the boolean equivalent of addition. The sum of two positive numbers is non-zero if either number is non-zero. In words, the OR function states: "If A OR B is true then C is true". Like AND, the OR function is commutative.
{{clear}}
{{clear}}
[[Category:Mathematics]]
== See Also ==
*[http://www.learn-c.com/boolean.htm Boolean logic tutorial]
[[Category:Logic]]
[[Category:Computer Science]]
[[Category:Electronics]]
[[Category:Electronics]]