Introduction of K-Map (Karnaugh Map) - GeeksforGeeks

K-map can take two forms Sum of Product (SOP) and Product of Sum (POS) according to the need of problem. K-map is table like representation but ... 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ImproveArticle SaveArticle LikeArticle DifficultyLevel: EasyLastUpdated: 15Jun,2022Inmanydigitalcircuitsandpracticalproblemsweneedtofindexpressionwithminimumvariables.WecanminimizeBooleanexpressionsof3,4variablesveryeasilyusingK-mapwithoutusinganyBooleanalgebratheorems.K-mapcantaketwoformsSumofProduct(SOP)andProductofSum(POS)accordingtotheneedofproblem.K-mapistablelikerepresentationbutitgivesmoreinformationthanTRUTHTABLE.WefillgridofK-mapwith0’sand1’sthensolveitbymakinggroups.StepstosolveexpressionusingK-map- SelectK-mapaccordingtothenumberofvariables.Identifymintermsormaxtermsasgiveninproblem.ForSOPput1’sinblocksofK-maprespectivetotheminterms(0’selsewhere).ForPOSput0’sinblocksofK-maprespectivetothemaxterms(1’selsewhere).Makerectangulargroupscontainingtotaltermsinpoweroftwolike2,4,8..(except1)andtrytocoverasmanyelementsasyoucaninonegroup.Fromthegroupsmadeinstep5findtheproducttermsandsumthemupforSOPform.SOPFORM:1.K-mapof3variables–K-mapSOPformfor3variablesZ=∑A,B,C(1,3,6,7) Fromredgroupwegetproductterm— A’C Fromgreengroupwegetproductterm— AB Summingtheseproductterms weget- Finalexpression(A’C+AB)  2.K-mapfor4variables–K-map4variableSOPformF(P,Q,R,S)=∑(0,2,5,7,8,10,13,15) Fromredgroupwegetproductterm— QS Fromgreengroupwegetproductterm— Q’S’ Summing theseproductterms weget- Finalexpression(QS+Q’S’)  POSFORM:1.K-mapof3variables–K-map3variablePOSformF(A,B,C)=π(0,3,6,7) Fromredgroupwefind terms A   B   Takingcomplementofthesetwo A'     B'   Nowsumupthem (A'+B') Frombrowngroupwefind terms B  C Takingcomplementofthesetwoterms B’ C’ Nowsumupthem (B’+C’) Fromyellowgroupwefindterms A'B'C’ Takingcomplementofthesetwo ABC Nowsumupthem (A+B+C) Wewilltakeproductofthesethreeterms:Finalexpression–(A'+B’)(B’+C’)(A+B+C) 2.K-mapof 4variables– K-map4variablePOSformF(A,B,C,D)=π(3,5,7,8,10,11,12,13)   Fromgreengroupwefind terms C’ D B Takingtheircomplementandsummingthem (C+D’+B’) Fromredgroupwefindterms C D A’ Takingtheircomplementandsummingthem (C’+D’+A) Fromblue groupwefind termsA C’ D’ Takingtheircomplementandsummingthem (A’+C+D) Frombrown groupwefind termsA B’ C Takingtheircomplementandsummingthem (A’+B+C’) Finallyweexpresstheseasproduct–(C+D’+B’).(C’+D’+A).(A’+C+D).(A’+B+C’) PITFALL– *AlwaysrememberPOS≠(SOP)’ *Thecorrectformis(POSofF)=(SOPofF’)’ QuizonK-MAP ThisarticleiscontributedbyAnujBhatam.Pleasewritecommentsifyoufindanythingincorrect,oryouwanttosharemoreinformationaboutthetopicdiscussedabove MyPersonalNotes 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