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# Class Note for ECE 274 with Professor Lysecky at UA 2

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COURSE
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TYPE
Class Notes
PAGES
7
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KARMA
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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 29 views.

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Date Created: 02/06/15
ECE 274 Digital Logic Lecmre 10 Lecmre 10 7 Chapter 4 9 Tabular Methode Minimiza m ECE 274 Digital Logic Tabular Memod for Minimizaum e QuinerMcQuskey Developed in me mldVSO39S Find me mimmized representauon of a Boolean function Provides systemauc Way of generaung all prime lmpllcanB men extracting a mll ilmum set ofprimes covering me Ol l39Set Accomplishes mi by repeatedly applw39ig me Urimrig meorem Urimrig meorem ab ab39 abb39 3 1 3 ECE 274 Digital Logic QuinerMcGusKey Algorimm QumeMeCiuskey Algorimm 1 Find all me prime implicams 2 Find all me essemai prlmelmpllcanls 3 Selecta minmai setofremainng prl me impiicaris matcovers remainrig 15 ECE 274 Digital Logic uinerMcCiLsKe 733mm Minimize F a39b39c39 a39 39c ab39c abc39 abc Step Fiin aii me pii me impiicai iB List aii eieiiimcs 7 unset and dm39ttaie set ieuesmm as a binaiv numba cmup iiiinreiiiis standing in the rumba Di 139s iri me iiiirinaiii m mm an mm 22 2222mmiim2m2imm2is 2M mm a mum Wei225iim2mii22i 2hr sm 62 gm W 22 i We cmquot W is 25 awn sun 2 mm 62 mm W63225iimm2222i5 ms wows smiegy Wiiihe p Us coware me imam svsimaiicaiy ECE 274 Digital Logic QuinerMcCiLskey e Exampie 1 Step 1 Fiiid aii the pii me impiicaris cont campaie am my iri Gi in each em iri Gin mm r1va lbiiwe an 2mm uniiingimmm 2nd eiimimie 2 iieni m mm Miniemmpim in Mind 2 ihzi ii mi 2 Vim imam mmbmd Ni 2mm eiemeni in 7m 2 i2igei mpiiani n nun en nix nnr nu neWimpiicameaie ueneiaiedrend 7 Dis12pi l nm 6 l539m s m 62 57 H WEhainuundaiimimeimpiicams s m 57 7 uneswnhuuicheckmaiks 7 m ECE 274 Digital Logic QuinerMcCiLsKeyrExampie l Step 2 Find aii essermai prime impiirai iir ieace DYimEim itanIEHait Dims 2m New meme mpiiani wedgein F a b c39 a39b39c ab c abc39 abc nun um um iin iii I n i 5 s 7 mm mm 57 57 7 derived In Step1 ECE 274 Digital Logic uii39ierMcClLsKe 7 Example Step 2 Fiin all essermai prime implicai iB cont Place x m a 7an me nime ileiEantEDvEs me mintam Essemal DiimE imuicams EYE fumd lJV lacking mi 7 mm a simie x minim i mm him we mm pm mpim e il39 m emmi me We mi Add Essemal UimE impiicams in me my essemia Dri me impiims quot 5 5 7 Ewei m we 7 n l539 l 57 H x 57 7 ECE 274 Digital Logic QuinerMcClLsKey 7 Example 1 Step 3 seiecta mii7imai set oi 7emamii7g prime impiicariis matoovers iemaming 1 sea 2 necammaa assmnai DiimE impiicancs and emu in ma Emmi Dime mplizm mm mm mimequot7 mm Mi zll minlevm mvved w lhe Vim mpim Mnlevm mimm in be oilied W m w W M a I 7 n 57 H ECE 274 Digital Logic QuirierMcClLsKeyrExame l Step 3 seieaa minimai seLoi remainrig mme impiicariis maicwers the an setome imam mt Easad Uri mm mintams ave lE add minimal 5a Ci DYlmE imditanis m Diva omv mimeim 5 iemainsr EnhEi mime irmiicam 15 mm WillWDik nlnnr CWquot ECE 274 Digital Logic uinerMcClLsKe 7 Example istnisan opuinai soiuuon7 1 YES 1 We generam all me nimenns and make sue they are all covered byme prime implicanis is me soluuon unique7 1 NOT FELISSARILV There could be afferent 565 of minimum covers ECE 274 Digital Logic QuinerMLClLskey 7 Example 2 lVlll Hlee F W39Xyz W39Xyz W39X39yz39 W39Xy39z39 W39xyz W39Xyz39 wxyz nyz Wx39y39z Wx39yz List all Elemmfs ufunset 2rd mm cave set veuesemad as a binaiv rumba Smp 1 Find all me pllme impiimm GmuD mintams amulan m the mmba Bf 139s in the mintam ism 1mm WW1 nnnnn is z m W39X39vx p KJWH 0mm WW ZJHMH W WM mm mm m mm mm m shun Wm 11m 63 mm wxvx 5 1111 J W m mm Wm M m 1511111 11 ECE 274 Digital Logic QuinerMcClLsKeyrEXample 2 Smp 1 Find all me pnine inipiicam omt mm m mm in ei in gain Em in em My r1va 1 we waving wingiim m1 inimie 1 iimi 111 Min mnwnnvim Mm 1 imi ii i mi W Mimi 61 mm 33 a I mm 61 mm 7111i I mm a z mm W a mi mm W a I mm A u l 25an a 2711151 11 62 mm 2 mm 1111315 mm 1911 1 91mm on a I 3quot 39 nu 311 m nunewimplicamsave W 31 1 57n1r EenEvaledrendms pl 11 mi nu ii 4 911 m 13 um 2ng I 112101 7 lt9 63 715 6 191111 mi mm 33 4 13151 m D 51 12 ECE 274 Digital Logic ulnerMCClLsKe 7 Example Step 2 Flle all essermal prime lmpllcal iB caste DYlmElm ltamd BYt Diem m mmm m me pm mplianl we deem me Plate x m a ian me UimE implitantmvas the mintam Essemal DYlmE impicams EYE fumd lJV lacking mi YUM mm a slmle x m emmisi Vim mam ia Ah My essmiisi prime mpicanis n z 3 i s 7 s n is is W quot265 M J x X wow mp n x g x x mm m x a mums H ECE 274 Digital Logic QuinerMcClLsKey 7 Example 2 Step 3 Selecta miiiimai semi remainiig prime implicarvis maicweis me on setoime mmuon Cmss nutall mimeims mead bv the UimE impiiarics Easad an mm mmcams aie left add minimal set at DYlmE imdicanis in my MlMEYm 3 and 7 YEWlniEllhEYPWWE impiicam 23M uilt3i7iiii15 Willqu mm s H Wquot F Wt wz VX mm M g x 37lms l g x mums 14 ECE 274 Digital Logic QuinerMcClLsKeyrExampe VWatifdeErminirvg minimum prime implicantoover is notso easV Assume We have me implicantlzble below DataminE Dime implitan add in Diva essemiapiime impiims n s 7 x a l3 15 V in m EM m m x WW 57 m six m1 x x ms an x ms m x ECE 274 Digital Logic mnerMLC LsKe 7 Examptej Examp e 3 emf Rana2 rmntams tweed m U me mums Leavz Emwntas rm7 m13 2rd ml Wh th Vemmmg VWe mdmm hmM we use to damn the mmmum mvu7 ns7x9x3xs 25 mm W m on F W m 57 m 913 m 715 an x x3 is m x m ECE 274 Dlgltal Loglc QuwmrMchsKeyrExamLie 3 Parmk s Manna fused m daenmne mwmmum wer 7 3 5 1 Radute Dnme muhcantchavt bv ammnngpnmemmammam V mnespmamm 5 g 3 139 v3 ms 1n g u 2 Labd mm m mum Fume muhtant mavtP1P2 WE quotH 8 3 Fam DQm E uannnmwmwstuevhm V W m 2H mum ave mm 7 Mo mm mm mm mm m 4 Rammmmmwmnfpmm m y Momxmmonmommoml WW3 N mundvmg nmandaw wm x xv x y m minnommom VAonm m y Mom szom 5 Sam cam msdunumwvzms a 39 mvamgsmunun y 7172mo71mo737273omm mm mm v evmmnezz z axe 73 P2 Em twig m m m MMquot 7 Wm W 7m m meemshan m m We WW WWW WWW 17 ECE 274 Dlgltal Loglc QumerMcC LsKeyrExam e3 7 x3 5 Fma cover essenna p mewmphcan s mmmum pnme m wcantower p m m g Essenh Vume mphcanS 2 mu m1 3 w v 715 an I a M mmumvume mphcamcwe s rm quot 3 WW WWW Wm WWW y Mnmommommomm mm mme meemshan m m We WW WWW WWW Minimixed Equation F w39y139 x39yx xyz wyz ECE 274 Digital Logic cm m 4 summer rogqmwzaum ofLogc Funcnons Kamaugh Maps maps xmomuemw apea ed Funcnons Dm39tcares Mum eve Sm hesws Panama menna Demmwsmm Mum eve Anew muea Represermon QumerMcQusKey Huck Dmv dz mule EXEWD ES D aem m mmum Ema sham YEW dtmmantE 19

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