NOR logic - Wikipedia

Making other gates by using NOR gates NORlogic FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch ThisarticleisaboutNORLogicinthesenseofbuildingotherlogicgatesusingjustNORgates.ForNORgates,seeNORgate.ForNORinthepurelylogicalsense,seeLogicalNOR.Forlogicgatesingeneral,seeLogicgate. Thisarticleneedsadditionalcitationsforverification.Pleasehelpimprovethisarticlebyaddingcitationstoreliablesources.Unsourcedmaterialmaybechallengedandremoved.Findsources: "NORlogic" – news ·newspapers ·books ·scholar ·JSTOR(November2014)(Learnhowandwhentoremovethistemplatemessage) AsingleNORgate ANORgateoraNOTORgateisalogicgatewhichgivesapositiveoutputonlywhenbothinputsarenegative. LikeNANDgates,NORgatesareso-called"universalgates"thatcanbecombinedtoformanyotherkindoflogicgate.Forexample,thefirstembeddedsystem,theApolloGuidanceComputer,wasbuiltexclusivelyfromNORgates,about5,600intotalforthelaterversions.Today,integratedcircuitsarenotconstructedexclusivelyfromasingletypeofgate.Instead,EDAtoolsareusedtoconvertthedescriptionofalogicalcircuittoanetlistofcomplexgates(standardcells)ortransistors(fullcustomapproach). Contents 1NOR 2MakingothergatesbyusingNORgates 2.1NOT 2.2OR 2.3AND 2.4NAND 2.5XNOR 2.6XOR 3Seealso 4References NOR[edit] Mainarticle:NORgate ANORgateislogicallyaninvertedORgate.Ithasthefollowingtruthtable: Q=ANORB TruthTable InputA InputB OutputQ 0 0 1 0 1 0 1 0 0 1 1 0 MakingothergatesbyusingNORgates[edit] ANORgateisauniversalgate,meaningthatanyothergatecanberepresentedasacombinationofNORgates. NOT[edit] Seealso:NOTgate ThisismadebyjoiningtheinputsofaNORgate.AsaNORgateisequivalenttoanORgateleadingtoNOTgate,joiningtheinputsmakestheoutputofthe"OR"partoftheNORgatethesameastheinput,eliminatingitfromconsiderationandleavingonlytheNOTpart. DesiredNOTGate NORConstruction Q=NOT(A) =ANORA TruthTable InputA OutputQ 0 1 1 0 OR[edit] Seealso:ORgate AnORgateismadebyinvertingtheoutputofaNORgate.NotethatwealreadyknowthataNOTgateisequivalenttoaNORgatewithitsinputsjoined. DesiredORGate NORConstruction Q=AORB =(ANORB)NOR(ANORB) TruthTable InputA InputB OutputQ 0 0 0 0 1 1 1 0 1 1 1 1 AND[edit] Seealso:ANDgate AnANDgategivesa1outputwhenbothinputsare1.Therefore,anANDgateismadebyinvertingtheinputsofaNORgate.Again,notethataNOTgateisequivalenttoaNORwithitsinputsjoined. DesiredANDGate NORConstruction Q=AANDB =(ANORA)NOR(BNORB) TruthTable InputA InputB OutputQ 0 0 0 0 1 0 1 0 0 1 1 1 NAND[edit] Seealso:NANDgate ANANDgateismadebyinvertingtheoutputofanANDgate.ThewordNANDmeansthatitisnotAND.Asthenamesuggests,itwillgive0whenboththeinputsare1. DesiredNANDGate NORConstruction Q=ANANDB =[(ANORA)NOR(BNORB)]NOR[(ANORA)NOR(BNORB)] TruthTable InputA InputB OutputQ 0 0 1 0 1 1 1 0 1 1 1 0 XNOR[edit] Seealso:XNORgate AnXNORgateismadebyconnectingfourNORgatesasshownbelow.ThisconstructionentailsapropagationdelaythreetimesthatofasingleNORgate. DesiredXNORGate NORConstruction Q=AXNORB =[ANOR(ANORB)]NOR[BNOR(ANORB)] TruthTable InputA InputB OutputQ 0 0 1 0 1 0 1 0 0 1 1 1 Alternatively,anXNORgateismadebyconsideringtheconjunctivenormalform ( A + B ¯ ) ⋅ ( A ¯ + B ) {\displaystyle(A+{\overline{B}})\cdot({\overline{A}}+B)} ,notingfromdeMorgan'sLawthataNORgateisaninverted-inputANDgate.Thisconstructionusesfivegatesinsteadoffour. DesiredGate NORConstruction Q=AXNORB =[BNOR(ANORA)]NOR[ANOR(BNORB)] XOR[edit] Seealso:XORgate AnXORgateismadebyconsideringtheconjunctivenormalform ( A + B ) ⋅ ( A ¯ + B ¯ ) {\displaystyle(A+B)\cdot({\overline{A}}+{\overline{B}})} ,notingfromdeMorgan'sLawthataNORgateisaninverted-inputANDgate.ThisconstructionentailsapropagationdelaythreetimesthatofasingleNORgateandusesfivegates. DesiredXORGate NORConstruction Q=AXORB =[(ANORA)NOR(BNORB)]NOR(ANORB) TruthTable InputA InputB OutputQ 0 0 0 0 1 1 1 0 1 1 1 0 Alternatively,the4-gateversionoftheXNORgatecanbeusedwithaninverter.Thisconstructionhasapropagationdelayfourtimes(insteadofthreetimes)thatofasingleNORgate. DesiredGate NORConstruction Q=AXORB ={[ANOR(ANORB)]NOR[BNOR(ANORB)]}NOR{[ANOR(ANORB)]NOR[BNOR(ANORB)]} Seealso[edit] NANDlogic—LikeNORgates,NANDgatesarealsouniversalgates. Functionalcompleteness References[edit] Retrievedfrom"https://en.wikipedia.org/w/index.php?title=NOR_logic&oldid=1086746523" Categories:LogicgatesHiddencategories:ArticlesneedingadditionalreferencesfromNovember2014Allarticlesneedingadditionalreferences Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk English Views ReadEditViewhistory More Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Languages EspañolLatinaLombard Editlinks