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Lexikon


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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