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Lexikon


two-valued logic


(Commonly known as "href="module.php?name=Lexikon&file=search&eid=1&query=Boolean algebra">Boolean algebra") A mathematical system concerning the two href="module.php?name=Lexikon&file=search&eid=1&query=truth values">truth values, TRUE and FALSE and the functions href="module.php?name=Lexikon&file=search&eid=1&query=AND">AND, href="module.php?name=Lexikon&file=search&eid=1&query=OR">OR, href="module.php?name=Lexikon&file=search&eid=1&query=NOT">NOT. Two-valued logic is one of the cornerstones of href="module.php?name=Lexikon&file=search&eid=1&query=logic">logic and is also fundamental in the design of href="module.php?name=Lexikon&file=search&eid=1&query=digital electronics">digital electronics and href="module.php?name=Lexikon&file=search&eid=1&query=programming languages">programming languages. The term "Boolean" is used here with its common meaning - two-valued, though strictly href="module.php?name=Lexikon&file=search&eid=1&query=Boolean algebra">Boolean algebra is more general than this. Boolean functions are usually represented by href="module.php?name=Lexikon&file=search&eid=1&query=truth tables">truth tables where "0" represents "false" and "1" represents "true". E.g.: A | B | A AND B --+---+-------- 0 | 0 | 0 0 | 1 | 0 1 | 0 | 0 1 | 1 | 1 This can be given more compactly using "x" to mean "don' t care" (either true or false): A | B | A AND B --+---+-------- 0 | x | 0 x | 0 | 0 1 | 1 | 1 Similarly: A | NOT A A | B | A OR B --+------ --+---+-------- 0 | 1 0 | 0 | 0 1 | 0 x | 1 | 1 1 | x | 1 Other functions such as href="module.php?name=Lexikon&file=search&eid=1&query=XOR">XOR, href="module.php?name=Lexikon&file=search&eid=1&query=NAND">NAND, href="module.php?name=Lexikon&file=search&eid=1&query=NOR">NOR or functions of more than two inputs can be constructed using combinations of AND, OR, and NOT. AND and OR can be constructed from each other using href="module.php?name=Lexikon&file=search&eid=1&query=DeMorgan' s Theorem">DeMorgan' s Theorem: A OR B = NOT ((NOT A) AND (NOT B)) A AND B = NOT ((NOT A) OR (NOT B)) In fact any Boolean function can be constructed using just NOR or just NAND using the identities: NOT A = A NOR A A OR B = NOT (A NOR B) and href="module.php?name=Lexikon&file=search&eid=1&query=DeMorgan' s Theorem">DeMorgan' s Theorem. (2003-06-18)

In addition suitable contents:
[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=396">ag ] [ href="module.php?name=Lexikon&op=content&tid=432">AL ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=464">algebra ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=603">AND ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=1025">B ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1181">be ] [ href="module.php?name=Lexikon&op=content&tid=1269">bi ] [ href="module.php?name=Lexikon&op=content&tid=1480">Boolean ] [ href="module.php?name=Lexikon&op=content&tid=1481">Boolean algebra ] [ href="module.php?name=Lexikon&op=content&tid=1535">br ] [ href="module.php?name=Lexikon&op=content&tid=1695">by ] [ href="module.php?name=Lexikon&op=content&tid=1708">C ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2330">com ] [ href="module.php?name=Lexikon&op=content&tid=2332">combination ] [ href="module.php?name=Lexikon&op=content&tid=2410">compact ] [ href="module.php?name=Lexikon&op=content&tid=2545">con ] [ href="module.php?name=Lexikon&op=content&tid=2606">cons ] [ href="module.php?name=Lexikon&op=content&tid=2976">D ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3304">design ] [ href="module.php?name=Lexikon&op=content&tid=3384">digit ] [ href="module.php?name=Lexikon&op=content&tid=3386">digital ] [ href="module.php?name=Lexikon&op=content&tid=3565">do ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3834">E ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=3986">electron ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4150">era ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4379">fact ] [ href="module.php?name=Lexikon&op=content&tid=4393">FALSE ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4828">fr ] [ href="module.php?name=Lexikon&op=content&tid=4940">function ] [ href="module.php?name=Lexikon&op=content&tid=4989">ga ] [ href="module.php?name=Lexikon&op=content&tid=5057">ge ] [ href="module.php?name=Lexikon&op=content&tid=5070">gen ] [ href="module.php?name=Lexikon&op=content&tid=5134">gh ] [ href="module.php?name=Lexikon&op=content&tid=5141">gi ] [ href="module.php?name=Lexikon&op=content&tid=5205">gn ] [ href="module.php?name=Lexikon&op=content&tid=5291">gr ] [ href="module.php?name=Lexikon&op=content&tid=5403">gu ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=5956">ie ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6165">input ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6861">kn ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=6950">language ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7399">ls ] [ href="module.php?name=Lexikon&op=content&tid=7402">LSE ] [ href="module.php?name=Lexikon&op=content&tid=7415">lu ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7457">M ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=7932">mil ] [ href="module.php?name=Lexikon&op=content&tid=8019">mm ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8167">mp ] [ href="module.php?name=Lexikon&op=content&tid=8384">N ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8403">NAND ] [ href="module.php?name=Lexikon&op=content&tid=8460">nc ] [ href="module.php?name=Lexikon&op=content&tid=8468">ND ] [ href="module.php?name=Lexikon&op=content&tid=8472">ne ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8630">ni ] [ href="module.php?name=Lexikon&op=content&tid=8660">nl ] [ href="module.php?name=Lexikon&op=content&tid=8675">no ] [ href="module.php?name=Lexikon&op=content&tid=8713">NOR ] [ href="module.php?name=Lexikon&op=content&tid=8728">NOT ] [ href="module.php?name=Lexikon&op=content&tid=8745">np ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=8820">O ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=9100">OR ] [ href="module.php?name=Lexikon&op=content&tid=9120">org ] [ href="module.php?name=Lexikon&op=content&tid=9160">OT ] [ href="module.php?name=Lexikon&op=content&tid=9204">pa ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9908">pr ] [ href="module.php?name=Lexikon&op=content&tid=10023">program ] [ href="module.php?name=Lexikon&op=content&tid=10042">programming ] [ href="module.php?name=Lexikon&op=content&tid=10044">programming language ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10754">rl ] [ href="module.php?name=Lexikon&op=content&tid=10767">ro ] [ href="module.php?name=Lexikon&op=content&tid=10887">ru ] [ href="module.php?name=Lexikon&op=content&tid=10918">S ] [ href="module.php?name=Lexikon&op=content&tid=11149">SE ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11389">sig ] [ href="module.php?name=Lexikon&op=content&tid=11651">so ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=12090">strict ] [ href="module.php?name=Lexikon&op=content&tid=12109">struct ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12246">sy ] [ href="module.php?name=Lexikon&op=content&tid=12312">system ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12360"> ] [ href="module.php?name=Lexikon&op=content&tid=12369">table ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12734">tone ] [ href="module.php?name=Lexikon&op=content&tid=12787">tr ] [ href="module.php?name=Lexikon&op=content&tid=12873">tron ] [ href="module.php?name=Lexikon&op=content&tid=12885">truth table ] [ href="module.php?name=Lexikon&op=content&tid=12939">tw ] [ href="module.php?name=Lexikon&op=content&tid=12986">ua ] [ href="module.php?name=Lexikon&op=content&tid=13008">ug ] [ href="module.php?name=Lexikon&op=content&tid=13175">us ] [ href="module.php?name=Lexikon&op=content&tid=13252">va ] [ href="module.php?name=Lexikon&op=content&tid=13260">value ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ] [ href="module.php?name=Lexikon&op=content&tid=13891">X ]






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