ENGG32AHomeworkAssignments(fromthe5theditionofthetextbook)

HW1--Ch1:7,10,11,15,16,and25.

Ch3:52,54,and55.

HW2--Ch2:1,2,6,7,8,and9.

Ch3:16and17.

UseCircuitVerse,adigitalsimulator,tocreatethetestcircuitsandtruthtablesof3-inputOR,AND,NAND,NOR,XOR,andXNORgates.(Note:Needtosubmitall8inputpatternsforeachgateinyourreport.Thismeansthattherewillbeatotalof48simulationcircuitsforthese8gates.Yourreportwillalsoincludeonetruthtablesummarizingtheoutputsofthe8circuitsofeverygate.)

Afterward,createthetestcircuitsandtruthtablesinordertoprovetheDeMorgan’stheoremof𝑋𝑌𝑍$$$$$$ = 𝑋$ + 𝑌$ + �̅�and𝐴 + 𝐵 + 𝐶 + 𝐷$$$$$$$$$$$$$$$$$$$ = �̅� ∙ 𝐵$ ∙ �̅� ∙ 𝐷-inp.7ofLectureNote#2.(Note:AllIneedarejustonesimulationcircuitforleftsideandonesimulationcircuitfortherightsideofeachoneofthetwoexpressions.Then,yourreportshowsthatthetruthtablesoftheleft-sidecircuitandright-sidecircuitoftheexpressionareidenticalinordertoprovethetheorem.)

HW3--Ch2:10,15,17,18,20,22,and26.

UseCircuitVersetocreatethetestcircuitsandtruthtablesinordertoprovetheConsensusTheoremof𝑋𝑌 + 𝑋$𝑍 + 𝑌𝑍 = 𝑋𝑌 + 𝑋$𝑍and(𝑋 + 𝑌)(𝑋$ + 𝑍)(𝑌 + 𝑍) =(𝑋 + 𝑌)(𝑋$ + 𝑍)inp.9ofLectureNote#2.(Note:AllIneedarejustonesimulationcircuitforleftsideandonesimulationcircuitfortherightsideofeachoneofthetwoexpressions.Then,yourreportshowsthatthetruthtablesoftheleft-sidecircuitandtheright-sidecircuitoftheexpressionareidenticalinordertoprovethetheorem.)

Afterward, create the test circuits and truth tables to prove that the 4-NAND-gate circuit in p. 14 of Lecture Note #2 is identical to a 2-input XOR gate. (Note: Need to submit 4 simulation circuits with the four input patterns to the 4-NAND-gate circuit. Then, your report shows that the truth table is identical to that of the XOR gate.)

Simulatethe8-biteven-paritygeneratorandcheckerinp.16ofLectureNote#2.(Note:Givefourexamplesoftheinputpatternstothesimulationcircuitstoshowthatthegeneratorandcheckerareworkingasexpected.Notruthtableisneeded.)

HW4--Ch3:1,2,8,10,29,44,46,47,and48.

UseCircuitVersetocreatetheBCDdecoderand7-segmentdisplaycircuitusingtheequationinp.10ofLectureNote3.[First,select“NewCircuit+”undertheCircuitmenu.Then,buildtheBCDdecoderwith4“inputindicators”asinputsand8“outputindicators”asoutputs.Afterward,addtheBCDcircuitasasub-circuitbyselecting“Main,”“InsertSubCircuit”undertheCircuitmenu,andfinallyselectthe“BCDdecoder”circuit.Add4“inputindicators”astheinputsanda7-segmentdisplayastheoutputsofthesubcircuit.Showfoursimulationcircuitswith4differentBCDinputpatternsinyourreport.]

UseCircuitVersetocreatethe4-bitAdder-Subtractorinp.27ofLectureNote3.(UsetheSubCircuitfeaturetobuildoneFullAdderfirst.Then,connectfourFullAdderinachaintocreatea4-bitAddersubcircuit.Finally,createthe4-bitAdder-Subtractorbyusingthis4-bitAddersubcircuit.Showthesimulationcircuitswithoneexampleofadditionandoneexampleofsubtractioninyourreport.)

HW5–Ch4:4,6,7,9,10,11,26,and33.

UseCircuitVersetocreatethepositive-edge-triggeredDflip-flopinp.7ofLectureNote4asasubcircuit.Connectthe“inputindicators”totheDandclockinputsandthe“outputindicator”totheQoutput.TestthecircuittomakesurethatthecontentofD-inputisstoredandshowsupattheQ-outputwheneverthereisarisingedgeintheclockinput.

Afterward,usethesubcircuitsofyour“positive-edge-triggeredDflip-flop”and“BCD-to-7-segmentconverter”(fromHW4)tocreatetheSequenceGeneratorinpp.25-27ofLectureNote4.Selectthe“Clock”inthe“SequentialElements”menuofCircuitVerseandconnectittotheclockinputsofthethreeDflip-flops.SettheClockTimeofthecircuitto1,000ms.Youshouldseethedigits0,1,4,2,and6cyclingthroughthe7-segmentdisplay,onedigitpersecond.

(Important:TheABCDinputsofyour“BCD-to-7-segmentconverter”isoppositetotheABCDinputsofthe“BCDdecoder”inp.27.Youwillneedtoreversetheconnectionsinthegeneratorcircuit.)

Includethescreenshotsofthesimulationcircuitsofthe“positive-edge-triggeredDflip-flop”andtheSequencewiththedigits4and2onthe7-segmentdisplayGeneratorinyourreport.

HW6–Ch6:5,11,12,15,16,andrepeat#16withTandalsoJKflip-flops.

Followthestepsinpp.20&21ofLectureNote5toimplementa2-digitaldecadecounterusingDflip-flops(notTflip-flops).YouwillneedtocreatefournewcolumnsinthestatetablefortheinputequationsoftheDflip-flops(toreplacethoseoftheTflip-flops).Afterward,applyK-maps(usingdon’tcaresintheunusedstates)toobtainthesimplestexpressionsofthefourinputequations.

UseCircuitVersetoimplementthefourinputequationsoftheDflip-flopsandtheexternaloutputequationYwithlogicgatesandfourDflip-flops,similartowhatyouhavedoneinHW5.

Totestyourcircuit,settheClockto1Hz(i.e.,1cyclepersecond=periodof1second).Then,the2-digitaldecadecountercancount100secondsfrom0to99repeatedly.Ifyousettheclockto100Hz(i.e.,100cyclepersecond=periodof10ms),itcancountevery1/100ofasecondandupto1second,potentiallyusefulasastopwatch.

Inyourreport,includethecompletedstatetable(withdon’tcaresintheunusedstates),fourinputequations,thesimulationcircuit,andthescreenshot(use“shift”“printscreen”tocapture)withthenumber89displayed.

HW7–Ch5:4,7,8,10,11,and13.

Ch7:1,8,and9.

Asadesignproject,asimple4-bitcentralprocessingunit(CPU)willbebuiltandsimulatedafterHW8.Beforethat,youneedtobuildthenecessarycomponentsas“subcircuits”inthisandnextassignment.Theyarethe2x4decoder(p.11ofLectureNote3),2x1MUX(p.20;don’tneedtheEnableinput),4x1MUX(p.19),4-bitparallelloadregister(p.3ofLectureNote5;usingfourofyourDflip-flopsubcircuit),and4-bitparalleladder(usingtheoneyoubuiltinHW4).

Buildthemassubcircuitsandtestthemcompletelytomakesurethattheyworkasexpected.Includeallthesesimulationcircuitsinyourreport.Includetwoscreenshotsofeachdeviceinthesubcircuitformwithtwodifferentinputcombinationstoshowthattheyworkproperly.

Foryourreference,belowaretheCircuitVersescreenshotsofthesimulationcircuits.

2x1Mux

4x1MUX 2x4Decoder

4-bitParallelLoadRegister

HW8--Ch6:19,20,22,24(usea4x1MUX),and31.

Ch8:4,5,9,10,and11.

Continuetobuildthenecessarycomponentsas“subcircuits”foryour4-bitCPUproject.Theyarethe4-bit2x1MUX,4-bit4x1MUX,1-bitlogiccircuit(p.18ofLectureNote7),and4-bitarithmeticcircuit(p.20ofLectureNote7;usingyour4-bitaddersubcircuit).

The4-bit2x1MUXsubcircuitisbuiltbyconnectingtheselectioninputSoffourofyour2x1MUXsubcircuittogetherasonecommonselectioninputSsothatthefinalsubcircuitissimilartop.21inLectureNote3buthereusingfourofyour2x1MUXsubcircuits.Makesuretolabeltheselectioninput,8datainputs,and4dataoutputsinyoursubcircuitproperly.Similarly,the4-bit4x1MUXisbuiltbyconnectingthetwoselectioninputsS1S0offourofyour4x1MUXsubcircuittogetherastwocommonselectioninputsS1S0.Makesuretolabelthetwoselectioninputs,16datainputs,and16dataoutputsinyoursubcircuitproperly.

Buildthemassubcircuitsandtestthemcompletelytomakesurethattheyworkasexpected.Includeallthesesimulationcircuitsinyourreport.Includetwoscreenshotsofeachdeviceinthesubcircuitformwithtwodifferentinputcombinations.

Foryourreference,belowaretheCircuitVersescreenshotsofthesimulationcircuits.

1-BitLogicCircuit

4-Bit4x1MUX 4-Bit2x1MUX

4-BitArithmeticCircuit

FinalProject:Asimple4-bitcentralprocessingunitwillbebuiltandsimulated.Thiswillaccountforthe8%ofyourgrade.

Continuetobuildthenecessarycomponentsas“subcircuits”foryour4-bitCPUproject.Theyarethe4-bitlogiccircuit(usingfourofyour“1-stagelogiccircuit”subcircuit)and4-bitALU(pp.17ofLectureNote7;usingyour“4-bitarithmeticcircuit”subcircuit,andone4-bit2x1MUXsubcircuit).Theinternalconfigurationofthis4-bitALUisshowninp.18,whichonlyshowstheconnectionofonestage(i.e.,onebit).Youhavetomakeit4stagesforthe4-bitALU.

Buildthemassubcircuitsandtestthemcompletelytomakesurethattheyworkasexpected.Includethesesimulationcircuitsinyourreport.Includetwoscreenshotsofeachdeviceinthesubcircuitformwithtwodifferentinputcombinations.

Foryourreference,belowaretheCircuitVersescreenshotsofthesimulationcircuits.

4-BitLogicCircuit

4-bitALU

This4-bitALUcanperformthefollowingmicro-operationsbysettingS2S1S0Cinaccordingly.

18

Now,connectyoursubcircuitsaccordingtothefollowingdiagramofthe4-bitCPU.Groupalltheinputsandoutputstogetherforeaseofcontrolandtesting.(Notetheclockinputandexternaldatainputs.)

Foryourreference,theCircuitVersescreenshotoftheCPUisshowninnextpage.Payattentiontohowalltheinputsandoutputsaregroupedtogether.

A B D F

n = 4

22

4

2

Input datan

I3 I2 I1 I0

O3 O2 O1 O0

n=4

Input indicators

output indicators

Input indicator

Input indicator A

Input indicator F

Input indicator B

Input indicator D

This4-bitCPUiscontrtolledbythebitsof“AMUXselect,”“BMUXselect,”“Ddestinationselect,”and“Foperationselect.”Theyaregroupedtogethertoformthecontrolword.

Controlword:

Toexecuteaninstruction(ormicro-operation)ofauserprogram,thecorrespondingcontrolwordwillbestoredintoanInstructionRegister(IR),whoseoutputsareconnectedtotheselectioninputsofthetwoMUXes,decoderofthethreeregisters,andALU(e.g.,seetheupperrightcornerofthesimulationcircuit).

A B D F

n = 4

22

4

2

Input datan

I3 I2 I1 I0

O3 O2 O1 O0

n=4

Input indicators

output indicators

Input indicator

Input indicator A

Input indicator F

Input indicator B

Input indicator D

A1 A0 B1 B0 D1 D0 S2 S1 S0 Cin

ThefollowingtablessummarizehowthesourceanddestinationregistersandtheALUoperationsareselectedbysettingthebitsatA,B,D,andFsectionsofthecontrolword.

A B D00 R0 R0 R001 R1 R1 R110 R2 R2 R211 input input --

S2S1S0 Cin=0 Cin=1000 F=A F=A+1001 F=A+B F=A+B+1010 F=A+𝐵 F=A-B011 F=A-1 F=A100 F=AandB 101 F=AorB 110 F=AxorB 111 F=𝐴

Toexecuteonemicro-operation(orinstructionofauserprogram),youfirstloadthecontrolwordintotheIR.Inthesimulation,thisisdonebysettingtheinputindicatorsoftheIRaccordingtothebitpatternofthecontrolword.

Forexamples,themicro-operationsandcontrolwordstosetR0=4andR1=3:

first,setexternalinput=0100 firstsetexternalinput=0011Microoperation: R0ßinput R1ßinputField: A B D F A B D FSymbol: input -- R0 A input -- R1 AControlword: 11 11 00 0000 11 11 01 0000Microoperation: R2ßR0orR1 R2ßR0-R1Field: A B D F A B D FSymbol: R0 R1 R2 AorB R0 R1 R2 A-BControlword: ? ? ? ? 00 01 10 0101Microoperation: R1ßR0 R2ßR0+R1Field: A B D F A B D FSymbol: R0 -- R1 A R0 R1 R2 A+BControlword: ? ? ? ? ? ? ? ?--=don’tcarecondition.Forsimplicity,hereletitbe11.

Wehavecoveredtheworkingprincipleofthe4-bitALU.Nowisthetimetotestyoursimulationcircuit.Youaregoingtoperformthefollowingtests,whichincludeonelogicoperation(i.e.,or),onesubtraction(i.e.,4-3),andonemultiplication(i.e.,4x3):

1. Loadaninteger4(i.e.,0100)fromtheexternalinputintoR0inoneclockcycle.(Warning:Tosimulateoneclockcycle,youneedtoclicktheclockinputindicatorfrom0to1andthenbackto0(onetimeonly)togeneratearisingedgeattheclockinputoftheregisters.Onlydothis0-1-0clockcycleonceforeachmicro-operation.)Youshouldseetheresult,CoutF3F2F1F0=00100,atthefiveoutputindicatorsconnectingtotheALUoutputandthedigit“4”onthe7-segmentdisplay.

2. Loadaninteger3(i.e.,0011)fromtheexternalinputintoR1inanotherclockcycle(i.e.,0-1-0clockcycleonce.)YoushouldseeCoutF3F2F1F0=0011andthedigit“3”.

3. Perform“R0orR1”andstoretheresultintoR2inoneclockcycle.YoushouldseeCoutF3F2F1F0=00111anddigit“7”.)

4. Perform“R0-R1”andstoretheresultintoR2inoneclockcycle.(Youshouldseetheresult,10001,atthefiveoutputindicatorsconnectingtotheALUoutput.Don’tworryabouttheCout=1,whichmeansthesumispositivewhenperformsubtraction.)

5. TransferthecontentofR0toR1.(Note:Steps5-7willperformthe4x3multiplication.)

6. perform“R0+R1”andstoretheresultintoR2inoneclockcycle.(Youshouldseetheresult,01000(=8),atthefiveoutputindicatorsconnectingtotheALUoutput.)

7. perform“R0+R2”againandstoretheresultintoR1inoneclockcycle.(Youshouldseetheresult,01100(=12),atthefiveoutputindicatorsconnectingtotheALUoutput.)

Writeyourprogram(i.e.,controlwords)inthefollowingtable(nextpage)andthenexecutethemonebyone.FirstsettheinputindicatorsI3I2I1I0tothebitpatternoftheexternalinputandthentheinputindicatorsattheIRtothebitpatternofthecontrolword.

Afterward,clicktheclockinputindicatorfrom0to1andthenbackto0togeneratearisingedgeattheclockinputoftheregisters.(Warning:Onlydo0-1-0onceattheclockinputforeachcontrolword.)Then,youhavecompletedtheexecutionofonecontrolword.

Theresultisshownatthe4outputindicatorsconnectingtotheALUoutput.Recordthebitpatternofthe4outputindicatorsinthetable.

Micro-Operations ExternalInput(I3I2I1I0)

ControlWords ALUOutput(CoutF3F2F1F0)afterone0-1-0clockcycle

R0ßinput(0100) 0100 1111000000 00100R1ßinput(0011) 0011 R2ßR0vR1 -- R2ßR0-R1 -- 10001R1ßR0 -- 00100R2ßR0+R1 -- R1ßR0+R2 --

Includethesimulationcircuitsofthe4-bitlogiccircuitandALUinyourreport.Includetwoscreenshotsofeachdeviceinthesubcircuitformwithtwodifferentinputcombinations.

Includingtheabovetableinthereport.Alsoincludethescreenshotsofthewhole4-bitCPUwiththeALUoutputshowingthe(correct)resultsofthemicro-operationsinthetable.