two-valued logic
(Commonly known As "<A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=BooleAn AlgebrA">BooleAn AlgebrAA>") A mAthemAticAl system concerning the two <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=truth vAlues">truth vAluesA>, TRUE And FALSE And the functions <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=AND">ANDA>, <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=OR">ORA>, <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=NOT">NOTA>. Two-vAlued logic is one of the cornerstones of <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=logic">logicA> And is Also fundAmentAl in the design of <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=digitAl electronics">digitAl electronicsA> And <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=progrAmming lAnguAges">progrAmming lAnguAgesA>. The term "BooleAn" is used here with its common meAning - two-vAlued, though strictly <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=BooleAn AlgebrA">BooleAn AlgebrAA> is more generAl thAn this. BooleAn functions Are usuAlly represented by <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=truth tAbles">truth tAblesA> 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 <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=XOR">XORA>, <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=NAND">NANDA>, <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=NOR">NORA> 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 <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=DeMorgAn' s Theorem">DeMorgAn' s TheoremA>: 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 <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=DeMorgAn' s Theorem">DeMorgAn' s TheoremA>. (2003-06-18) Align="left">In Addition suitAble contents:
[ <A href="module.php?nAme=Lexikon&op=content&tid=31">2A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=134">=A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=396">AgA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=432">ALA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=433">AlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=464">AlgebrAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=544">AmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=592">AnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=603">ANDA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=740">ArA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=743">ArcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=800">AsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=894">AtA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1025">BA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1026">bA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1181">beA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1269">biA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1480">BooleAnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1481">BooleAn AlgebrAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1535">brA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1695">byA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1708">CA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1724">cAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2001">chA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2247">coA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2330">comA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2332">combinAtionA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2410">compActA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2545">conA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2606">consA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2976">DA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3151">deA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3304">designA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3384">digitA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3386">digitAlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3565">doA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3752">duA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3834">EA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3865">ecA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3896">edA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3986">electronA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4148">erA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4150">erAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4171">esA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4379">fActA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4393">FALSEA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4497">fiA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4520">fileA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4828">frA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4940">functionA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4989">gAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5057">geA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5070">genA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5134">ghA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5141">giA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5205">gnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5291">grA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5403">guA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5434">hA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5768">hrA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5931">idA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5956">ieA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6013">ilA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6064">inA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6165">inputA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6413">ioA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6482">isA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6558">itA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6861">knA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6918">lAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6950">lAnguAgeA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7091">LexA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7399">lsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7402">LSEA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7415">luA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7441">lyA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7457">MA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7463">mAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7932">milA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8019">mmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8032">moA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8040">modA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8079">moduleA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8167">mpA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8384">NA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8386">nAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8403">NANDA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8460">ncA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8468">NDA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8472">neA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8627">ngA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8630">niA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8660">nlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8675">noA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8713">NORA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8728">NOTA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8745">npA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8760">nsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8820">OA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8964">omA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9100">ORA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9120">orgA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9160">OTA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9204">pAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9550">phA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9908">prA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10023">progrAmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10042">progrAmmingA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10044">progrAmming lAnguAgeA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10253">queryA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10364">rcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10385">reA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10754">rlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10767">roA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10887">ruA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10918">SA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11149">SEA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11150">seA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11376">siA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11389">sigA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11651">soA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11934">stA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12090">strictA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12109">structA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12133">suA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12246">syA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12312">systemA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12359">TA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12360"> A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12369">tAbleA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12588">thA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12721">toA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12734">toneA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12787">trA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12873">tronA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12885">truth tAbleA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12939">twA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12986">uAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13008">ugA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13175">usA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13252">vAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13260">vAlueA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13310">veA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13891">XA> ]
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