Universal Logic Gates and Complete Sets - Electronics Tutorials

Any logic gate which can be combined into a set to realise all other logical functions is said to be a universal gate with a complete logic set being a ... X Registertodownloadpremiumcontent! Registertodownloadpremiumcontent! X Deutsch Polski Register LogIn ACCircuits Amplifiers Attenuators BinaryNumbers BooleanAlgebra Capacitors CombinationalLogic Connectivity Counters DCCircuits Diodes Electromagnetism Filters Inductors Input/OutputDevices LogicGates MiscellaneousCircuits OperationalAmplifiers Oscillator PowerElectronics PowerSupplies Premium RCNetworks Resistors Resources SequentialLogic Systems Transformers Transistors Uncategorized WaveformGenerators PremiumContent FurtherEducation Sitemap ContactUs Home / LogicGates / UniversalLogicGates UniversalLogicGates UniversalLogicgatescanbeusedtoproduceanyotherlogicorBooleanfunctionwiththeNANDandNORgatesbeingminimal Individuallogicgatescanbeconnectedtogethertoformavarietyofdifferentswitchingfunctionsandcombinationallogiccircuits.AswehaveseenthroughtthisDigitalLogictutorialsection,thethreemostbasiclogicgatesarethe:AND,ORandNOTgates,andgiventhissetoflogicgatesitispossibletoimplementallofthepossibleBooleanswitchingfunctions,thusmakingthema“fullset”ofUniversalLogicGates. Byusinglogicalsetsinthisway,thevariouslawsandtheoremsofBooleanAlgebracanbeimplementedwithacompletesetoflogicgates.Infact,itispossibletoproduceeveryotherBooleanfunctionusingjustthesetofANDandNOTgatessincetheORfunctioncanbecreatedusingjustthesetwogates.Likewise,thesetofORandNOTcanbeusedtocreatetheANDfunction. Anylogicgatewhichcanbecombinedintoasettorealiseallotherlogicalfunctionsissaidtobeauniversalgatewithacompletelogicsetbeingagroupofgatesthatcanbeusedtoformanyotherlogicfunction. Forexample,ANDandNOTconstituteacompletesetoflogic,asdoesORandNOTascascadingtogetheranANDwithaNOTgatewouldgiveusaNANDgate.SimilarlycascadinganORandNOTgatetogetherwillproduceaNORgate,andsoon.However,thetwofunctionsofANDandORontheirowndonotformacompletelogicset. SobyusingthesethreeUniversalLogicGateswecancreatearangeofotherBooleanfunctionsandgates.However,theNANDandNORgatesareclassedasminimalsetsbecausetheyhavethepropertyofbeingacompletesetinthemselvessincetheycanbeusedindividuallyortogethertoconstructmanyotherlogiccircuits.Thereforewecandefinethecompletesetsofoperationsofthemainlogicgatesasfollows: AND,ORandNOT(aFullSet) ANDandNOT(aCompleteSet) ORandNOT(aCompleteSet) NAND(aMinimalSet) NOR(aMinimalSet) Thuswecanusethesefivesetsofgates,togetherorindividuallyasthebuildingblockstoproducemorecomplexlogiccircuitscalledcombinationallogiccircuits.Butfirstletusremindourselvesoftheswitchingcharacteristicsofthethreebasiclogicgates,AND,ORandNOT. TheANDFunction Inmathematics,thenumberorquantityobtainedbymultiplyingtwo(ormore)numberstogetheriscalledtheproduct.InBooleanAlgebratheANDfunctionistheequivalentofmultiplicationandsoitsoutputstaterepresentstheproductofitsinputs.TheANDfunctionisrepresentedinBooleanAlgebrabyasingle“dot”(.)soforatwoinputANDgatetheBooleanequationisgivenas:Q = A.B,thatisQequalsbothAANDB. The2-inputLogicANDGate SymbolTruthTable BAQ 000 010 100 111 TheORFunction Inmathematics,thenumberorquantityobtainedbyaddingtwo(ormore)numberstogetheriscalledthesum.InBooleanAlgebratheORfunctionistheequivalentofadditionsoitsoutputstaterepresentstheadditionofitsinputs.InBooleanAlgebratheORfunctionisrepresentedbya“plus”sign(+)soforatwoinputORgatetheBooleanequationisgivenas:Q = A+B,thatisQequalseitherAORB. The2-inputLogicORGate SymbolTruthTable BAQ 000 011 101 111 TheNOTFunction TheNOTgate,whichisalsoknownasan“inverter”isgivenasymbolwhoseshapeisthatofatrianglepointingtotherightwithacircleatitsend.Thiscircleisknownasan“inversionbubble”. TheNOTfunctionisnotadecisionmakinglogicgateliketheAND,orORgates,butinsteadisusedtoinvertorcomplementadigitalsignal.Inotherwords,itsoutputstatewillalwaysbetheoppositeofitsinputstate. TheNOTgatesymbolhasasingleinputandasingleoutputasshown. TheLogicNOTGate SymbolTruthTable AQ 01 10   ThesingleinputNOTgateorinvertfunctioncanbecascadedwithitselftoproducewhatiscalledadigitalbuffer.ThefirstNOTgatewillinverttheinputandthesecondwillre-invertitbacktoitsoriginallevelperformingadoubleinversionofthesingleinput.Non-invertingDigitalBuffershavemanyusesindigitalelectronicsasthisdoubleinversionoftheinputcanbeusedtoprovidedigitalamplificationandcircuitisolation. UsingtheANDandNOTSet UsingjusttheANDandNOTsetoflogicgateswecancreatethefollowingBooleanfunctionsandequivalentgates. UniversalLogicGatesAND/NOTSetEquivalents UsingtheORandNOTSet UsingtheORandNOTsetoflogicgateswecancreatethefollowingBooleanfunctionsandequivalentgates. OR/NOTSetEquivalents UsingtheFullAND,ORandNOTSet UsingthefullAND,ORandNOTsetoflogicgateswecancreatetheBooleanexpressionsfortheExclusive-OR(Ex-OR)andtheNOTExclusive-OR(Ex-NOR)gatesasshown. FullAND/OR/NOTSettoImplementEx-OR   FullAND/OR/NOTSettoImplementEx-NOR   NotethatneithertheExclusive-ORgateortheExclusive-NORgatecanbeclassedasauniversallogicgateastheycannotbeusedontheirownortogethertoproduceanyotherBooleanfunction. UniversalLogicGates OneofthemaindisdvantagesofusingthecompletesetsofAND,ORandNOTgatesisthattoproduceanyequivalentlogicgateorfunctionwerequiretwo(ormore)differenttypesoflogicgate,ANDandNOT,orORandNOT,orallthreeasshownabove.However,wecanrealisealloftheotherBooleanfunctionsandgatesbyusingjustonesingletypeofuniversallogicgate,theNAND(NOT AND)ortheNOR(NOT OR)gate,therebyreducingthenumberofdifferenttypesoflogicgatesrequired,andalsothecost. TheNANDandNORgatesarethecomplementsofthepreviousANDandORfunctionsrespectivelyandareindividuallyacompletesetoflogicastheycanbeusedtoimplementanyotherBooleanfunctionorgate.Butaswecanconstructotherlogicswitchingfunctionsusingjustthesegatesontheirown,theyarebothcalledaminimalsetofgates.ThustheNANDandtheNORgatesarecommonlyreferredtoasUniversalLogicGates. ImplementationofUniversalLogicGatesFunctionUsingOnlyNAND The7400(orthe74LS00or74HC00)quad2-inputNANDTTLchiphasfourindividualNANDgateswithinasingleICpackage.Thuswecanuseasingle7400TTLchiptoproducealltheBooleanfunctionsfromaNOTgatetoaNORgateasshown. UniversalLogicGatesusingonlyNANDGates   ThusALLotherlogicgatefunctionscanbecreatedusingonlyNANDgatesmakingitauniversallogicgate. ImplementationofUniversalLogicGatesFunctionUsingOnlyNOR The7402(orthe74LS02or74HC02)quad2-inputNORTTLchiphasfourindividualNORgateswithinasingleICpackage.Thusliketheprevious7400NANDICwecanuseasingle7402TTLchiptoproducealltheBooleanfunctionsfromasingleNOTgatetoaNANDgateasshown. UniversalLogicGatesusingonlyNORGates   ThusALLotherlogicgatefunctionscanbecreatedusingonlyNORgatesmakingitalsoauniversallogicgate. NotealsothattheimplementationoftheExclusive-ORgateismoreefficientusingNANDgatescomparedtousingNORgates,whiletheimplementationoftheExclusive-NORgateismoreefficientwithNORgatescomparedtousingNANDgatesasineachcaseonlyfourindividuallogicgatesarerequired.InotherwordswecancreatealltheBooleanfunctionsusingjustone7400NANDorone7402NORchipincludingitsvarioussub-families. PreviousPull-upResistors ReadmoreTutorialsinLogicGates 1.DigitalLogicGates 2.LogicANDGateTutorial 3.LogicORGateTutorial 4.LogicNOTGateTutorial 5.LogicNANDGateTutorial 6.LogicNORGateTutorial 7.Exclusive-ORGateTutorial 8.Exclusive-NORGateTutorial 9.DigitalBufferTutorial 10.DigitalLogicGatesSummary 11.Pull-upResistors 12.UniversalLogicGates 48Comments JointheconversationCancelreplyError!Pleasefillallfields. Notifymeoffollow-upcommentsbyemail. Δ TonyJoshua PlsIhavequestions PostedonJune27th2022|6:04am Reply Susmitha NiceandtovareynotebookwasathinkingwasmindaresupergoodmorningTimewasagooddaytempleinyourlifeatoaree PostedonJune20th2022|5:23am Reply HamdiKOSE Çokfaydalıteşekkürler. PostedonMay18th2022|6:52pm Reply NOMANZAHOOR Niceexplanation.SpeciallyANDgateusingnandgate.Notavailableontherwebsiteslikeelectrical4u, PostedonMay01st2022|6:22am Reply NadeemMohmand Bestinformation. PostedonFebruary14th2022|5:10pm Reply NelsonJoshua GreatsitewhichhelpedmealotsoIwanttojoin. PostedonNovember11th2021|4:33am Reply Abubakarasani Wonderful…!!!! Reallyappreciateit…… PostedonSeptember08th2021|11:16pm Reply dave Iamcuriousifitpossibletouseonlyanotgatetomakeanothergatetype.Evenifyouhavetouseaknownmaskandanaddorsubtractidea.Ihavenotbeenabletofindtalkonthis. PostedonAugust16th2021|8:44pm Reply Faheem Thesethings…clearlywritten…everyonecanunderstandeasily.lovethis🌼respectforthisguywhodidthis..🖤 PostedonApril18th2021|6:59am Reply RanaUmar Itwasagreat👍☺️experiencetochosethispage😊thanksalot🥰🥰butplzalsogivethetruthtablesoftheabovementionedtopic🥰🥰🥰 PostedonApril13th2021|4:53am Reply MuawiyaSadiq goodjobandniceclass PostedonApril05th2021|9:40pm Reply AmritNeupane Mitochondriaisthepowerhouseofcell Thankyou PostedonMarch30th2021|6:33am Reply ajaypareek howtoimplementthevariouslogicgateusinguniversalgate? PostedonMarch21st2021|5:02am Reply MD.Raihan F=xy+x’y’+y’z ImplementitwithAND,OR,&NOTgates PostedonFebruary18th2021|2:33pm Reply C E PostedonFebruary11th2021|3:18pm Reply naveed Q1:Whichgatesarecalledasuniversalgate,whysuchgatesarecalleduniversalgatesandwhatisitsusefulness? Q2:WhatisK-MapMethod,forwhichpurposeK-Mapisused?Whatareitsadvantagesanddisadvantages?AlsoexplaingroupingruleswhilemakingaK-MapforaBooleanexpressionalongwithexamplesforeachrule? PostedonFebruary01st2021|5:49am Reply Hassan Howcanyouimplementand/or/notgateusingAND/NOR PostedonJanuary22nd2021|8:05am Reply M youcanuseaninverterforthesubstitutiononnotgates PostedonMarch15th2021|8:45am Reply WayneStorr ANORgateiseffectivelyaNot-ORcombination PostedonJanuary22nd2021|3:32pm Reply KalyankumarChatterjee Applicationoflogicwithdigitalrelaycircuitwillbemorehelpfull Fortheprofessional. PostedonDecember27th2020|5:51pm Reply Shweta Nycanswers PostedonDecember16th2020|3:23pm Reply Siddu SwetaIloveu❤️❤️…pleasereplaytothis PostedonMarch13th2021|7:31am Reply FlorenceGwekwe Whataboutstimulation PostedonDecember07th2020|7:03am Reply ViewMore ReadmoreTutorialsinLogicGates 1.DigitalLogicGates 2.LogicANDGateTutorial 3.LogicORGateTutorial 4.LogicNOTGateTutorial 5.LogicNANDGateTutorial 6.LogicNORGateTutorial 7.Exclusive-ORGateTutorial 8.Exclusive-NORGateTutorial 9.DigitalBufferTutorial 10.DigitalLogicGatesSummary 11.Pull-upResistors 12.UniversalLogicGates LookingforDataSheets? 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