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1、SolutionsfortheEnd-of-the-ChapterProblemsinSwitchingandFiniteAutomataTheory,3rdEd.ZviKohaviandNirajK.JhaChapter11.2.(a)(16)10=(100)4(b)(292)10=(1204)61.4.(a)Numbersystemswithbaseb≥7.(b)Baseb=8.1.5.Themissingnumberis(31)5.Theseriesofintegersrepresentsnumber
2、(16)10indifferentnumbersystems.1.7.(a)Inapositivelyweightedcode,theonlywaytorepresentdecimalinteger1isbya1,andtheonlywaytorepresentdecimal2iseitherbya2orbyasumof1+1.Clearly,decimal9canbeexpressedonlyifthesumoftheweightsisequaltoorlargerthan9.(b)5211*5321431
3、1*632153117321631144214221*542152216421622174213321*84214321*denotesaself-complementingcode.Theabovelistexhaustsallthecombinationsofpositiveweightsthatcanbeabasisforacode.1.8.(a)Ifthesumoftheweightsislargerthan9,thenthecomplementofzerowillbew1+w2+w3+w4>9.I
4、fthesumissmallerthan9,thenitisnotavalidcode.1(b)751−4;832−4;652−4.1.9.(a)Fromthemaptobelow,itisevidentthatthecodecanbecompletedbyaddingthesequenceofcodewords:101,100,110,010.xyz0001111001(b)Thiscodecannotbecompleted,since001isnotadjacenttoeither100or110.xy
5、z0001111001(c)Thiscodecanbecompletedbyaddingthesequenceofcodewords:011,001,101,100.xyz0001111001(d)Thiscodecanbecompletedbyaddingcodewords:1110,1100,1000,1001,0001,0011,0111,0110,0010.1.13.(a)(i)A,C,andDdetectsingleerrors.(ii)CandDdetectdoubleerrors.(iii)A
6、andDdetecttripleerrors.(iv)CandDcorrectsingleerrors.(v)Noneofthecodescancorrectdoubleerrors.(vi)Dcorrectssingleanddetectsdoubleerrors.(b)Fourwords:1101,0111,1011,1110.Thissetisunique.2Chapter22.1.A:40%A,B:12%A,B,C:4%B:30%A,C:8%C:30%B,C:6%22%receivenocredit
7、.AB2481644220C222.2.ReflexiveSymmetricAntisymmetricTransitiveRelationname(a)yesyesnoyesequivalence(b)yesyesnonocompatibility(c)yesyesnoyesequivalence(d)yesnoyes*yespartialordering(e)yesnonoyes–(f)yesnonoyes–*dependsontheinterpretationofcongruence.2.4.(a)π1+
8、π2={a,b,c,g,h,i,j,k;d,e,f},π1·π2={a,b;c;d,e;f;g,h;i;j,k}(b)π1+π3=π3,π1·π3=π1(c)π1<{a,b,c;d,e;f;g,h,i,j,k}<π3(d)No,sinceπ2isnotgreaterthanorsmallerthanπ3.2.6.Lattice1isnotdistributive,becausec(b+d)=ca=cwhilecb
