CS231 Spring 2011_HW3_Solution

CS231 Spring 2011_HW3_Solution - CS231 Spring 2011 Homework...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS231 Spring 2011 Homework 3 Solution Circuit Design, Decoders and Multiplexers Due at 5:00pm, Wednesday, February 16, 2011 in CS231 HW boxes in Siebel Center's basement Introductory notes: Writeyourname,yournetID,and"CS231"clearlyonthefirstpage. YoumustfollowtheFormattingGuidelineslistedontheassignmentspage oryourscorewillbepenalized. Thereareatotalof6questionsinthishomeworkworthatotalof100points. Youmustworkindividuallyonhomework.Youmaydiscussmaterialwith otherstudents,theTAs,andtheProfessorforthepurposeofunderstanding, butyourworkmustbeyourown.Seethesyllabusforourcheatingpolicy. Thegeneralguidelinefordoingassignmentsisthatyoumustconvinceus thatyouknowwhatyou'redoing.Toreceivecredit,makesureyoursolutions areneatandlegible,andthatyoushowenoughwork. TurnintheassignmentintheHWboxes.TheHWboxesarelocatedinthe eastendofthebasementofSiebelCenter(nearthevendingmachines). Pleasedonotsubmititanywhereelse.Youmayturnintheassignmentupto 24hoursaftertheduedatei.e.by Thursday, Feb 17, at 5:00pm, but you will receive a 20% late penalty. HomeworkwillNOTbeacceptedafterthis(asthis iswhenwewillpostthesolutions).Seethesyllabusforourlatepolicy. Youareencouragedtousebookproblemsforpractice. Pleasestapleallyourpagestogetherwithareal,metalstaple. Feelfreetoaskusquestionsatofficehoursoronthecoursenewsgroup. 1.(8points)ThefollowingKmapsallattempttoshowthefunctionFwithdon't careconditionsX a. (4points)WhichKmapshaveinvalidgroupings?Explain. A:Impropergrouping(blue) B:Hasazero D:Hasagroupingthatisnotapowerof2 b. (4points)WhatistheminimumsumofproductsoffunctionF? X'Y'Z+WX'Y+YZ'+XZ'OR X'Y'Z+WX'Z+YZ'+XZ' 2.(12points)UseaKmaptoobtainaminimalsumofproducts(MSP)anda minimalproductofsums(MPS)ofthefollowingfunction.("d"meansdon'tcare.) F(W,X,Y,Z)=m(0,1,2,6,9,10,11,12) d(W,X,Y,Z)=m(5) (a)minimalsumofproducts(MSP) F(W,X,Y,Z)=WXY'Z'+W'X'Z'+X'Y'Z+W'YZ'+WX'YOR WXY'Z'+W'X'Y'+X'Y'Z+W'YZ'+WX'YOR WXY'Z'+WX'Z+WX'Y+W'X'Y'+W'YZ' (b)minimalproductofsums(MPS) F(W,X,Y,Z)= (W'+X+Y+Z)(W+Y'+Z')(W+X'+Y)(W'+X'+Y')(X'+Z') 3.(20points)Inthelecture,youlearnedthatNORgate(andalsoNANDgate)is calleduniversal,sinceitcanreplaceallothergates.Now,usingonlyNANDgates, showhowtobuild (a)(6points)aNORgate (b)(6points)anXORgate OR (c)(8points)aNXORgate(NOTXOR) OR 4.(20points)Considerf(a,b,c)=m(3,5,6)andg(a,b,c)=M(0,2,3). (a)(10points)Foreachfunction,drawthecorrespondingtwolevelcircuit,such thateachcircuithasseveral3inputANDgatesfeedingintoasingleORgate.Donot simplifytheexpression. f=A'BC+AB'C+ABC'g=A'BC+AB'C'+AB'C+ABC'+ABC (b)(10points)Foreachfunction,drawthecorrespondingtwolevelcircuit,such thateachcircuithasseveral3inputORgatesfeedingintoasingleANDgate.Donot simplifytheexpression. F=(A+B+C)(A+B+C')(A+B'+C)(A'+B+C)(A'+B'+C') G=(A+B+C)(A+B'+C')(A+B'+C) 5.(20points)AcombinationalcircuitisdefinedbythefollowingthreeBoolean functions: F1=(X+Z)'+XYZ F2=(XY)'Z F3=(X'+Z)'+X'Y'Z' DesignthecircuitwithadecoderandexternalORgates. F1=(X+Z)'+XYZ=X'Z'+XYZ=X'Y'Z'+X'YZ'+XYZ=m(0,2,7) F2=(XY)'Z=X'Z+Y'Z=X'Y'Z+X'YZ+XY'Z+X'Y'Z=m(1,3,5) F3=(X'+Z)'+X'Y'Z'=XZ'+X'Y'Z'=XY'Z'+XYZ'+X'Y'Z'=m(0,4,6) 6.(20points)AcombinationalcircuitisdefinedbythefollowingthreeBoolean functions: F1(X,Y,Z)=X+Z F2(X,Y,Z)=XY'+YZ+X'Z' F3(X,Y,Z)=XZ' ImplementF2andF3usingonlya3to8decoder,a2inputORgateanda2input NORgate. TheNORgatewillcomplementthesumoftwomintermssincethedecoder canonlyoutputminterms.ThereforewewillfindF'2intermsofthe mintermsandfeedthatintotheNORgatesowegetF2back. F'2=X'Y'Z+XYZ'=m(1,6) F3=XY'Z'+XYZ'=m(4,6) ...
View Full Document

Ask a homework question - tutors are online