NAND gate - Wikipedia

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Implementations NANDgate FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Logicalgate Input Output A B ANANDB 0 0 1 0 1 1 1 0 1 1 1 0 TheTTL7400chip,containingfourNANDs.Thetwoadditionalpinssupplypower(+5V)andconnecttheground Indigitalelectronics,aNANDgate(NOT-AND)isalogicgatewhichproducesanoutputwhichisfalseonlyifallitsinputsaretrue;thusitsoutputiscomplementtothatofanANDgate.ALOW(0)outputresultsonlyifalltheinputstothegateareHIGH(1);ifanyinputisLOW(0),aHIGH(1)outputresults.ANANDgateismadeusingtransistorsandjunctiondiodes.ByDeMorgan'slaws,atwo-inputNANDgate'slogicmaybeexpressedasA•B=A+B,makingaNANDgateequivalenttoinvertersfollowedbyanORgate. TheNANDgateissignificantbecauseanybooleanfunctioncanbeimplementedbyusingacombinationofNANDgates.Thispropertyiscalledfunctionalcompleteness.ItsharesthispropertywiththeNORgate.DigitalsystemsemployingcertainlogiccircuitstakeadvantageofNAND'sfunctionalcompleteness. ThefunctionNAND(a1,a2,...,an)islogicallyequivalenttoNOT(a1ANDa2AND...ANDan). OnewayofexpressingANANDBis A ∧ B ¯ {\displaystyle{\overline{A\landB}}} ,wherethesymbol ∧ {\displaystyle{\land}} signifiesANDandthebarsignifiesthenegationoftheexpressionunderit:inessence,simply ¬ ( A ∧ B ) {\displaystyle{\displaystyle\neg(A\landB)}} . NANDgateswithtwoormoreinputsareavailableasintegratedcircuitsintransistor-transistorlogic,CMOS,andotherlogicfamilies. Contents 1Symbols 2Hardwaredescriptionandpinout 2.1CMOSversion 2.1.1Availability 3Implementations 4Functionalcompleteness 5Seealso 6References 7Externallinks Symbols[edit] TherearethreesymbolsforNANDgates:theMIL/ANSIsymbol,theIECsymbolandthedeprecatedDINsymbolsometimesfoundonoldschematics.Formoreinformationseelogicgatesymbols.TheANSIsymbolfortheNANDgateisastandardANDgatewithaninversionbubbleconnected. MIL/ANSISymbol IECSymbol DINSymbol Hardwaredescriptionandpinout[edit] NANDgatesarebasiclogicgates,andassuchtheyarerecognisedinTTLandCMOSICs. DiagramoftheNANDgatesinaCMOStype4011integratedcircuit. CMOSversion[edit] Thestandard,4000series,CMOSICisthe4011,whichincludesfourindependent,two-input,NANDgates. Availability[edit] ThesedevicesareavailablefrommostsemiconductormanufacturerssuchasFairchildSemiconductor,PhilipsorTexasInstruments.Theseareusuallyavailableinboththrough-holeDILandSOICformat.Datasheetsarereadilyavailableinmostdatasheetdatabases. Thestandard2-,3-,4-and8-inputNANDgatesareavailable: CMOS 4011:Quad2-inputNANDgate 4023:Triple3-inputNANDgate 4012:Dual4-inputNANDgate 4068:Mono8-inputNANDgate TTL 7400:Quad2-inputNANDgate 7410:Triple3-inputNANDgate 7420:Dual4-inputNANDgate 7430:Mono8-inputNANDgate Implementations[edit] NMOSNANDgate PMOSNANDgate CMOSNANDgate TTLNANDgate ThephysicallayoutofaCMOSNAND Dieofa74AHC00Dquad2-inputNANDgatemanufacturedbyNXPSemiconductors Siliconimplementationof4NANDgatesinanintegratedcircuit Functionalcompleteness[edit] Mainarticle:NANDlogic TheNANDgatehasthepropertyoffunctionalcompleteness,whichitshareswiththeNORgate.Thatis,anyotherlogicfunction(AND,OR,etc.)canbeimplementedusingonlyNANDgates.[1]AnentireprocessorcanbecreatedusingNANDgatesalone.InTTLICsusingmultiple-emittertransistors,italsorequiresfewertransistorsthanaNORgate. AsNORgatesarealsofunctionallycomplete,ifnospecificNANDgatesareavailable,onecanbemadefromNORgatesusingNORlogic.[1] Desiredgate NORConstruction Seealso[edit] Shefferstroke ANDgate ORgate NOTgate NORgate XORgate XNORgate NORlogic Booleanalgebra Flashmemory References[edit] ^abMano,M.MorrisandCharlesR.Kime.LogicandComputerDesignFundamentals,ThirdEdition.PrenticeHall,2004.p.73. Externallinks[edit] TTLNANDandANDgates–AllAboutCircuits WikimediaCommonshasmediarelatedtoNANDgates. vteLogicalconnectives Tautology/True  ⊤ {\displaystyle\top} Alternativedenial (NANDgate)  ↑ {\displaystyle\uparrow} Converseimplication  ← {\displaystyle\leftarrow} Implication (IMPLYgate)  → {\displaystyle\rightarrow} Disjunction (ORgate)  ∨ {\displaystyle\lor} Negation (NOTgate)  ¬ {\displaystyle\neg} Exclusiveor (XORgate)  ↮ {\displaystyle\not\leftrightarrow} Biconditional (XNORgate)  ↔ {\displaystyle\leftrightarrow} Statement (Digitalbuffer) Jointdenial (NORgate)  ↓ {\displaystyle\downarrow} Nonimplication (NIMPLYgate)  ↛ {\displaystyle\nrightarrow} Conversenonimplication  ↚ {\displaystyle\nleftarrow} Conjunction (ANDgate)  ∧ {\displaystyle\land} Contradiction/False  ⊥ {\displaystyle\bot}  Philosophyportal Retrievedfrom"https://en.wikipedia.org/w/index.php?title=NAND_gate&oldid=1096441766" Categories:LogicgatesHiddencategories:ArticleswithshortdescriptionShortdescriptionisdifferentfromWikidataCommonscategorylinkisonWikidataPagesthatuseadeprecatedformatofthemathtags Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk English Views ReadEditViewhistory More Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Inotherprojects WikimediaCommons Languages العربيةAzərbaycancaCatalàČeštinaDeutschEestiEspañolEsperantoEuskaraفارسیFrançais한국어हिन्दीHrvatskiItalianoעבריתLatinaLombardМакедонскиNederlands日本語PolskiPortuguêsRomânăSimpleEnglishSlovenčinaСрпски/srpskiSrpskohrvatski/српскохрватскиSuomiSvenskaதமிழ்TürkçeУкраїнськаTiếngViệt吴语粵語中文 Editlinks

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