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two-valued logic

(Commonly known as "Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=BoolEan algEbra">BoolEan algEbra") A mathEmatical systEm concErning thE two Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=truth valuEs">truth valuEs, TRUE and FALSE and thE functions Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=AND">AND, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=OR">OR, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=NOT">NOT. Two-valuEd logic is onE of thE cornErstonEs of Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=logic">logic and is also fundamEntal in thE dEsign of Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=digital ElEctronics">digital ElEctronics and Ef="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 Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=BoolEan algEbra">BoolEan algEbra is morE gEnEral than this. BoolEan functions arE usually rEprEsEntEd by Ef="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 Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=XOR">XOR, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=NAND">NAND, Ef="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 Ef="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 Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=DEMorgan' s ThEorEm">DEMorgan' s ThEorEm. (2003-06-18)

E="bordEr-width:thin; bordEr-color:#333333; bordEr-stylE:dashEd; padding:5px;" align="lEft">In addition suitablE contEnts:
[ Ef="modulE.php?namE=LExikon&op=contEnt&tid=31">2 ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=134">= ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=396">ag ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=432">AL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=433">al ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=464">algEbra ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=544">am ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=592">an ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=603">AND ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=740">ar ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=743">arc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=800">as ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=894">at ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1025">B ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1026">b ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1181">bE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1269">bi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1480">BoolEan ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1481">BoolEan algEbra ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1535">br ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1695">by ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1708">C ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1724">ca ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2001">ch ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2247">co ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2330">com ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2332">combination ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2410">compact ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2545">con ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2606">cons ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2976">D ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3151">dE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3304">dEsign ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3384">digit ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3386">digital ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3565">do ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3752">du ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3834">E ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3865">Ec ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3896">Ed ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3986">ElEctron ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4148">Er ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4150">Era ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4171">Es ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4379">fact ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4393">FALSE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4497">fi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4520">filE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4828">fr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4940">function ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4989">ga ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5057">gE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5070">gEn ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5134">gh ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5141">gi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5205">gn ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5291">gr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5403">gu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5434">h ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5768">hr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5931">id ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5956">iE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6013">il ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6064">in ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6165">input ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6413">io ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6482">is ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6558">it ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6861">kn ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6918">la ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6950">languagE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7091">LEx ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7399">ls ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7402">LSE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7415">lu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7441">ly ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7457">M ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7463">ma ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7932">mil ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8019">mm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8032">mo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8040">mod ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8079">modulE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8167">mp ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8384">N ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8386">na ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8403">NAND ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8460">nc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8468">ND ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8472">nE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8627">ng ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8630">ni ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8660">nl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8675">no ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8713">NOR ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8728">NOT ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8745">np ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8760">ns ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8820">O ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8964">om ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9100">OR ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9120">org ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9160">OT ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9204">pa ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9550">ph ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9908">pr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10023">program ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10042">programming ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10044">programming languagE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10253">quEry ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10364">rc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10385">rE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10754">rl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10767">ro ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10887">ru ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10918">S ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11149">SE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11150">sE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11376">si ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11389">sig ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11651">so ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11934">st ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12090">strict ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12109">struct ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12133">su ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12246">sy ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12312">systEm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12359">T ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12360"> ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12369">tablE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12588">th ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12721">to ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12734">tonE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12787">tr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12873">tron ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12885">truth tablE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12939">tw ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12986">ua ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13008">ug ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13175">us ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13252">va ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13260">valuE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13310">vE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13891">X ]

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