NAND and NOR | Spinning Numbers

NOR gate Weintroducetwonewgates,theNANDandNOR.Thesehaveadvantagesinsizeandspeedbecauseofthewaytransistorcircuitsimplementgates. WrittenbyWillyMcAllister. Contents NANDgate NORgate WhyarethereNANDandNORgates? Conceptcheck ThefirstadditionswemaketoourcollectionofsimplegatesareNANDandNOR. NANDgate ANANDgate(shortforNOT-AND)isthesameasANDfollowedbyNOT.Youcanseehowwe’vesquishedthesymbolstogether, TheequationforaNANDgateisC=A·B ThetruthtableforNANDistheoppositeofAND.Youlistthesameinputsbutinverttheoutputoneveryrow, ThereareafewwaystothinkabouttheNANDtruthtable. DescribewhentheoutputisTRUE:TheoutputisTRUEifanyoftheinputsareFALSE. DescribewhentheoutputisFALSE:TheoutputisFALSEifbothinputsareTRUE. NORgate ANORgate(NOT-OR)isthesameasORfollowedbyNOT.WemergetheORandNOTsymbolstogethertogetNOR, TheequationforaNORgateisC=A+B ThetruthtableforNORistheoppositeofOR.Youlistthesameinputsbutinverttheoutputoneveryrow, ThereareafewwaystothinkabouttheNORtruthtable. DescribewhentheoutputisTRUE:TheoutputisTRUEifbothoftheinputsareFALSE. DescribewhentheoutputisFALSE:TheoutputisFALSEifanyinputsareTRUE. WhyarethereNANDandNORgates? WhydowebothercreatingNANDandNORgates?WhynotjuststringtogetherAND,OR,andNOTwheneverweneedto?Wehaven’tcoveredhowtobuildlogicgatesyet,buttherearesomeverygoodreasonstodefineNANDandNOR, Electroniccircuitsarenaturallyinverting. WhetheryoubuildgateswithMOSFETsorBJTtransistors,thesimplestcircuittoimplementanANDorORfunctionsalsoinvertstheoutputsignal“forfree.”Ifyouwantanon-invertinggateyouhavetoaddaninvertertoundothe“free”inversion. Simpleissmaller. Youwanttousethefewesttransistorsandthefewestgatespossible.Onagatearray,semi-customASIC,orcustomintegratedcircuit,aNANDgateisalwayssmallerthananANDgate.ANORgateisalwayssmallerthananORgate. Simpleisfaster. ThenaturallyinvertingNANDgateisalwaysfasterthanaAND+NOTcombination. Simplesavepower. Simplegateshavefewernodesthathavetochangeeverylogictransition.Fewermovingnodesmeanslesschargeissloshingaround,whichmeanslesschargehastocomefromthepowersupply.Thatmeansyourbattery-powereddigitalgizmolastsalotlonger.Wouldn’titbeniceifyourmobilephonestayedchargedforamonthinsteadofaday? Learningtodesignwithinvertinggatesisabigwin.Wearegoingtocoverthatsoon. Conceptcheck WritedownthefourtruthtablesforANDNANDORNOR,side-by-side. Compareandcontrasttheoutputpatternstounderstandhowtheyaredifferent, Describewhichinputsmaketheoutput1. Describewhichinputsmaketheoutput0. Getusedtodescribinggatesindifferentways.Oftenwhenyoudesignlogicyoustartwithaverbaldescriptionofwhatyouwantandthentranslateitintogates. Summary TheequationforaNANDgateisC=A·B TheequationforaNORgateisC=A+B Evenifyouneverplantodesigndigitalhardware,itisgoodtoappreciatewhyinvertinggates(NANDandNOR)arepreferredforlogicdesign.Thesimplestgatesarenaturallyinverting.Simplegatesarefaster,smaller,anduselesspower.Ifyouareasoftwareperson,Iassureyounoneofyoursoftwarecolleaguesknowthis.Showoffyounewknowledge! Comment(cancelreply) Name E-mail Sendmeanemailwhensomeonecomments. Submit Commentsareheldformoderation.Therewillbeadelaybeforetheyappear. CommentsmayincludeMarkdown. Tosharesomethingprivately:Contactme. Close