lec06_f08 - \u AmEEmEU cuzo> gov mamEi mm 5505 cm $38.6...

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Unformatted text preview: :\u AmEEmEU cuzo> gov mamEi mm 5505.. cm? $38.6 0.52 EgamtfiEoo ; . “mmmv nmug. 9.: 95 mcorommcmhh mom Tum? 33 __mm an 69:25 :EosmEmfimE ucm EUREQ $2.654. , .33me 02.522 acetate 55... afiétqgm .69. 3052: taco < "$2. nEva. 9: ho mmczomwooi :flosmEmfimE $2.584. mums— ;msmme ho 205:.— :\. 3330.5 5230 mimeo Etgcoo muoo . _ mwimem :o_pmN_E_:_EEm_mon_ $30 “.200 62.398322 082 . 625 M £09 8.5-x monEOm .955: ">208 cmumétv $6955. Eofimwm 325.. 68598. «mam. mag; £20-50; ancafififloo. wucfiwhmccs 30> 53:. $02. $00 2920. .m> @5952 :80 Eofimsomfi ~30 2.2.22 "En m .33 5:35 mum xow>> 63:22 mum x925 _ "En. w .33... . . Nam 33 "En. m >200... :Boym b a. @ "mg—mt 03—9 @5595: MERE; w u w .owd mom 4 THREE VARIABLE EXAMPLE: FULL ADDER C B A 1. mo A I u 7 011 1’11 011 401.0 1" V m a a. 100 S 000 100 Gout ' 000 Cout : ABC’ + AB’C + ABC + ABC . S. As+nc+ec min SOP: S = AB’C’ + A’BC’ + A’B’C + ABC min SOP; / «6.2? . .\m much. . .. no?» 92 i 3 $3.: «a # :34 .o w 29.3: 525$ 05 mm: : .958 “.0 38:3: E:E_:_E a 5:5 m:o_wwm._:xm 9: m:oE< .N. _ "oven 92% L353: £551”... .64 o . 9.5.3 Hos—aemdu—o 32:5: E=E_:_E 9: mm: a. ._‘ fizamu : .mEEE 2 :ofiwwixm now :6. we: LOW ._<_>=Z=>_ ".0 ZO_._._Z_n_mD E «um 6.325% a $0 203.91.30.15 7 3395.0 w._<_>=z=>_ w. ._._:om=o :o__._>> mm Ex: EH F.» 3% OF HF ~Mu+m9x _ + nmum x I NEED . _ F0 00 N> NM $88 .1 mfix WK. LnMIIII-d - . Q - - a Q E? + N? + .N.>x + N>.x + .N>.x + N}qu [r'llllrl‘L a H F F F F w F o F F o F o F F o o F F F F , o F o F o F F o o o o o o Ncéx > cabofiuofimfifimué A.v mepmfig Eng n. , .Bfinaoo on :8 2E3, 585 fiufifl 8 023308 Hag Que-v.— A... was 53:. , .. . .058 fish a mo nouSqomofioHuFmfifiw m< Egon. now 5:86 Ems—Q: nas— smsmme 9:. F . .. H . F F. ._ ... .. FF .. F F. . F 3:30 Ewe—cam . MINIMAL soP EXPRESSIONS 3 - VARIABLE KARNAUGH MAPS q/ISIOE ‘ x Ix! ‘Ixa,axl yz (_)_[)_V_O_‘IH1‘IA~ 10 .oo 01 _.11 10 4-var. functions # of literals loop size yz 00A 01 ‘11“ 10 3-var functions ‘ . loop size # of literals # of cells KARNAUG H MAPS Alternative representation of truth tables: ‘ Lists cells in Gray code order (00, 01, 11, 10) Can ‘fsee” adjacencies in upto 6 dimensions 2 cells are adjacent iff they differ in 1 bit iff they can be “combined” Product terms <¢ loops ( = rectangles, cubes) l!‘l,H*),2-’2 11“,ng 10 Oyl I 00 013/211 10 00 O1yz“ 0 “HEM 00”“ mm 1 man wx 01 WNW f(x,y) f(x,y,z) 11 q“! ‘l/II .38.: . . chwmmw : $5 :2: .E .25 ago. 5 3.3.95 EEEE um; ~ ax}. swag ‘53 . .ma ammmmE =< .Emo=aE_ 392 m 555., to: 32m Ea: .maoo. . 23:00 5 ._... £3 Jun Fax; .3...» ... \mmma \m Is» In a. . .maoo. ._mm0,_. =< i=3 “260.5 2: yo wEEEE =5 .2 F o=_m> $5 mm: «550:3 05 t :osoczu. a DB Ellwoumg an m_ Ego“ «0:605 < 33/15/03 How TO USE A K-MAP TO FlND'A MINIMAL SOP A minimal SOP expression is a sum of prime implicants (Pls). It consists. of: - All the essential PJs - As few (other) Plsfxas possible Procedure: H 1. Find all essential‘éPls. For each 1 which Eihas not yet been circled: ' . is it covered by ionly one Pl? (l.e., is there “no choice” on how to circle-that 1?) If yes, that PI is essential and must be a term in any min SOP representation. Tips: Always look on all sides of the 1. As you find-each essential Pl, draw its loop. 2. Cover the remaining 1’s using as few Pls asfpossible. Look carefully: can all the 1’s be covered with 1 loop? With 2 loops? With 3 loops? “a /H ...
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This note was uploaded on 09/03/2009 for the course ECE 290 taught by Professor Brown during the Fall '08 term at University of Illinois at Urbana–Champaign.

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lec06_f08 - \u AmEEmEU cuzo> gov mamEi mm 5505 cm $38.6...

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