3 input XNOR gate operation

For 3 input XOR gate and XNOR gate, by solving the equations I got the result as in the picture. ... So according to the solution the outputs of ... ElectricalEngineeringStackExchangeisaquestionandanswersiteforelectronicsandelectricalengineeringprofessionals,students,andenthusiasts.Itonlytakesaminutetosignup. Signuptojointhiscommunity Anybodycanaskaquestion Anybodycananswer Thebestanswersarevotedupandrisetothetop Home Public Questions Tags Users Unanswered Teams StackOverflowforTeams –Startcollaboratingandsharingorganizationalknowledge. CreateafreeTeam WhyTeams? Teams CreatefreeTeam Teams Q&Aforwork Connectandshareknowledgewithinasinglelocationthatisstructuredandeasytosearch. Learnmore 3inputXNORgateoperation AskQuestion Asked 5years,5monthsago Modified 3years,5monthsago Viewed 28ktimes 6 2 \$\begingroup\$ For3inputXORgateandXNORgate,bysolvingtheequationsIgottheresultasinthepicture. Soaccordingtothesolutiontheoutputsofthe3inputXORandXNORgatesaresame.Thissolutionholdsgoodwhennumberofinputstothegatesareodd. ForthecaseofevennumberofinputsXORandXNORarecomplementtoeachother. WiththisassumptiontheanswertothecircuitinthepictureshouldbeoptionA,B,andC.butthecorrectanswerisD.Iamconfusedastohow? Thanksinadvanceforthehelp. digital-logicinput Share Cite Follow askedFeb9,2017at10:23 turtleturtle 13311goldbadge11silverbadge1010bronzebadges \$\endgroup\$ Addacomment  |  4Answers 4 Sortedby: Resettodefault Highestscore(default) Datemodified(newestfirst) Datecreated(oldestfirst) 11 \$\begingroup\$ Themisunderstandingisthat,givenXORasalogicgate,XNORisdefinedasbeingalwaysitsnegation. HavingdefinedyourXOR-3asanoddparitychecker(byacceptingtheminterm\$xyz\$-otherwiseitwouldbeaonehotchecker),thecorrectinterpretationofaXNOR-3wouldthenbeanevenparitychecker(aspointedbyBradman175).ThissimplymeansthattheexpressionforyouralgebraicXNOR-3isnotcorrectinthiscontext. Inotherwords,\$x\odoty\odotz\ne\text{XNOR-3}\$. Let'sobserveanimplementationthroughlogicgates. AthreewayXORgatecanbeimplementedwithaXOR-2itselfXORedwiththeremaininginput,andrememberthatanyXNORhasthentoberenderedasaXORinserieswithaNOTgate. Therefore,aXNOR-3implementationwouldbe: simulatethiscircuit–SchematiccreatedusingCircuitLab Thisyieldsatruthtablecoherentwiththefunctionalityexpectedabove(1whenthereareanevenamountofinputat1).ThisalsoshowsthatatripleXNORisalgebraicallyrenderedas $$ \text{XNOR-3}\buildreldef\over=\text{NOT}(\text{XOR-3})=\overline{(x\oplusy\oplusz)}=\overline{(xyz+\overline{x}\overline{y}z+\overline{x}y\overline{z}+x\overline{y}\overline{z})} $$ bycarefullyexpoundingallterms,youeventuallygettotheevenparitycheckerexpressionwhichis $$ \text{XNOR-3}=\overline{x}\overline{y}\overline{z}+\overline{x}yz+xy\overline{z}+x\overline{y}z $$ Itfollowsthat: $$\text{XNOR-3}=(x\oplusy)\odotz\nex\odoty\odotz$$ asmentionedinthebeginning. Share Cite Follow answeredFeb15,2017at14:11 vaugsvaugs 17111silverbadge66bronzebadges \$\endgroup\$ 2 \$\begingroup\$ Thanks,yesXNOR-3=NOT(XOR-3)makessenseratherthanx⊙y⊙z≠XNOR-3. \$\endgroup\$ – turtle Feb17,2017at5:36 \$\begingroup\$ NotethatthefunctionofXOR/XNORgateswithmorethan2inputsisnotwelldefined.Seeelectronics.stackexchange.com/questions/93713/… \$\endgroup\$ – ElliotAlderson Jan1,2021at14:43 Addacomment  |  4 \$\begingroup\$ XORformorethan2inputsisnotwelldefined. Fortwoinputs,XORyields1ifthetwoinputsaredifferent. forthreeinputs,shouldXORyield1ifallorsomeofthethreeinputsaredifferent? Share Cite Follow answeredFeb9,2017at12:37 dannyfdannyf 4,19211goldbadge66silverbadges99bronzebadges \$\endgroup\$ 3 \$\begingroup\$ Forthreeinputs,XORyields1foroddnumberof1'sattheinput. \$\endgroup\$ – turtle Feb9,2017at17:48 \$\begingroup\$ That'smyverypoint.IfyouthinkXORshouldyield1iftheinputsaredifferent,havingXORyields1foroddnumberof1'smakesnosense.NotthatIamadvocatingtooneortheotherapproach.ItissimplytoillustratethatXORformorethan2inputsisnotwelldefined. \$\endgroup\$ – dannyf Feb9,2017at18:10 \$\begingroup\$ Yes,maybe.That'sthereasonalsoIamlookinggforamoreconvincingexplanation.Asithelpstodefinethecomponentbetterintheprogramlater.!Andthanksfortheanswer. \$\endgroup\$ – turtle Feb10,2017at2:50 Addacomment  |  1 \$\begingroup\$ ThelastNXORgateneedstohaveanevenamountofinputshightooutputhigh.ThisisbecauseanormalXORgateonlyturnsonifanoddamountofinputsarehigh.Thetoptwopinscanneverbebothonoroffatthesametime,becausetheirinputsareconnectedrespectivelytothesameinputsandarethesametypeofgateexceptoneisinverted. Nowthingsshouldbeeasier. Share Cite Follow answeredFeb9,2017at10:29 Bradman175Bradman175 1,1731010silverbadges2020bronzebadges \$\endgroup\$ 3 \$\begingroup\$ IfItakethecaseasevennumberofinputsgives'1'attheoutput,thentheabovequestion'sanswerisD.ButwhenItriedtosolvebyalgebramethodandthenfindtheresult,thenanswerisA,BandC.WhereamImakingthemistake! \$\endgroup\$ – turtle Feb9,2017at11:07 \$\begingroup\$ @turtleUnfortunatelyIcan'treadthealgebrabecauseIhaven'tlearntit,butdidyouforgettoindicatethatthelastXORgateisinverted,thusbeingaNXOR? \$\endgroup\$ – Bradman175 Feb9,2017at12:59 \$\begingroup\$ thanksforthehelp.Ihaveconsideredthecomplimentpart.Butmaybemyunderstandingofthegateiswrong.Iamunabletofindexplanationtoconvincemysolutionbeingwrong:) \$\endgroup\$ – turtle Feb9,2017at17:47 Addacomment  |  -1 \$\begingroup\$ AccordingtocircuitdiagramoptionDiscorrect.ThereisnoneedtouseBooleanalgebraforthis.Justgothroughthecircuit.Outputof3-inputEXORgateisnotsameasthatfor3-inputEXNORgate. Share Cite Follow editedAug1,2017at16:29 JakubRakus 2,21555goldbadges1717silverbadges2626bronzebadges answeredAug1,2017at9:06 shashishashi 111bronzebadge \$\endgroup\$ Addacomment  |  Highlyactivequestion.Earn10reputation(notcountingtheassociationbonus)inordertoanswerthisquestion.Thereputationrequirementhelpsprotectthisquestionfromspamandnon-answeractivity. Nottheansweryou'relookingfor?Browseotherquestionstaggeddigital-logicinputoraskyourownquestion. TheOverflowBlog StackExchangesitesaregettingprettierfaster:IntroducingThemes Moneythatmovesatthespeedofinformation(Ep.462) FeaturedonMeta Testingnewtrafficmanagementtool Duplicatedvotesarebeingcleanedup 2022ModeratorElectionQ&A–QuestionCollection 2022CommunityModeratorElection 2022CommunityModeratorElectionResults Linked 1 3InputXNORgatemadewithXORandnotgates 37 HowisanXORwithmorethan2inputssupposedtowork? 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