Logic Design Laboratory Manual Adobe Acrobat File.

71 Pages·1997·1.17 MB·English

by  Peter M. Maurer

Table of Contents
Experiment 1: Elementary Boolean Functions..............................................................1
Experiment 2: The Properties of Boolean Functions.....................................................4
Experiment 3: Theorems and Canonical Forms............................................................6
Experiment 4: Two-Level Functions..............................................................................8
Experiment 5: Nand/Nor Implementations..................................................................10
Experiment 6: Adders and Subtractors........................................................................11
Experiment 7: Code Converters...................................................................................14
Experiment 8: Seven Segment Displays.......................................................................18
Experiment 9: Multi-Level NAND/NOR Circuits........................................................20
Experiment 10: Ripple Carry Adders...........................................................................24
Experiment 11: Carry Lookahead................................................................................26
Experiment 12: Adder/Subtractors...............................................................................28
Experiment 13: BCD Adders........................................................................................33
Experiment 14: Comparators.......................................................................................36
Experiment 15: Decoders and Demultiplexers.............................................................38
Experiment 16: Encoders and Multiplexers.................................................................42
Experiment 17: Hamming Codes.................................................................................45
Experiment 18: ROMs and PLAs.................................................................................49
Experiment 19: Flip-Flops...........................................................................................51
Experiment 20: Sequential Circuits.............................................................................57
Experiment 21: Registers.............................................................................................60
Experiment 22: Counters.............................................................................................63
Experiment 23: Random Access Memories..................................................................65
Experiment 24: Tristate Logic......................................................................................68
Experiment 1: Boolean Functions
Experiment 1:
Elementary Boolean Functions
Objective: retsaM eht yratnemele naelooB ,snoitcnuf dna nrael woh ot esu eht cisab serutaef foeht
.rotalum iLSDHF
Instructions: LDHFniW si dengised rof SM swodniW 1.3 dna swodniW .59 tI si demussa tahtuoy
gni n e ne g yirt dedgon fe vaefesolgaebem w wn hrbndoSoialo ndMnkarsankritioviWwne
siht .tnemirepxe ehT LDHF rotalumiS margorp si detacol ni eht FHDL system margorp
.puorg seipoC fo eht LDHFni Wnoitallat ssneitteksid dluohs eb elbaliava hguorhtruoy
.rotcurtsni ,ylevitanretlA uoy yam daolnwod eht noitallatsni margorp morf bewetis
lmth.ldhf/reruam~/ude.fsu.eesc.www//:ptth .stnemire p lrd xll oeeelamfsbiauwrg os ri.phT
.swoll o sfkao odlluo hmsargo rrpotalum ies h,tgninn unrehW
kcilC ereH oetr ekhcilC ere hkcilC ere hkcilC oetr ekhcilC eh ts isihT
to create a gnitsi x nenaepo to save to print nepoeht ”o recsaUM“
.tiucr iwcen tiucric your work your work. noitalumis button.
wodniw
ru oeypyT
.er ethiucric kcilC erehrof
.pleH
ru oeypyT
s rtoutpcneiv
ereh
noitalumiS
stluser
ra.eeprpeah
n auc o,yhs iuw ofyI
srot cteu vpr nueiovyas
meh tnu rdn a,eli fani
sih tgnis uecn ot alla
button
1
Experiment 1: Boolean Functions
oT ezirai lfilmeasfruoy htiw eht ,rotalum iestaerc a elpmis tiuc rgincitsisnoc fo aelgnis
DNA gate ..swoll o sfdaep y sttiiucr isc i hT
MyCircuit: circuit
inputs a,b
outputs q
gate1: and (a,b),q
endcircuit
,ndal eli ef s btaaanhlemet a.hts cstanEemet aLt DstfHaoFm r eoshfettartsu ltliiuc rsiichT
noita r,eepdooc dna na dnar e.pdoleif ehT lebal dleif yam eb .knalb sleb asLyawladne
htiw .snoloc fI a tnemetats sah on ,lebal neht ti tsum trats htiw a .knalb slebaLsyawla
trats ni nmuloc .1 ,seta Ghcus sa and evah owt ,sdnarepo na tupni tsil dna na tuptuo.tsil
,tne myeselnnlnoieoa t tnr soeri chelftvi ie,ewsoehseht nd eenrs ia ot psls etcuebsnmhieTl
.detti mey obasmesehtner aepht
eotTal u,emthiits uncer pinoc o wieothdatnl iudwmnias epy tg neih wtootlnlio fehttupni
vector area.
0,0
.sen iol wgtniwoll oef hntiatn owc odnluo hwsodn i”weca rnToitalumi Se“hT
I>0,0
2>0
ynA egnniilnn ihgteibw I> sniatnoc tupni depyt yb .uoy ynA enil gninnigeb htiw n>
. rdoe tc r ya u etble detuuhsohtpmTnrteti(iplusaotnoc n).r esb tmanuenser per
etareneG a etelpmoc hturt elbat rof eht dna etag ygbnir e gtennhietlw aornluoloioftfidda
.srotcev etoN taht lareves srotcev nac eb depyt ta ecno fi uoy etarapes meht htiw-imes
.snoloc
0,1;1,0;1,1
h ttonB i erghPnt isstulu sre urtonyirP .une meli Feh tn idnuo fs ihcih w,dnammoc
.se tgangiwol l eo rhfsotefl bhatt utrnt i drenptaareneG
gate2: or (a,b),q
gate3: xor (a,b),q
gate4: not a,q
gate5: nor (a,b),q
gate6: nand (a,b),q
gate7: buff a,q
2
Experiment 1: Boolean Functions
gate8: xnor (a,b),q
Results: .noitcn uhfc ar eosfelb ahttu rdtetni re phnntiruT
FHDL: sihT tnemirepxe sah decudortni lareves wen sepyt fo LDHF .stnemetats sA ehtelpmas
e hhtt inwig etbs utmiucr ihcc a,eetartsul lsitiucric circuit .tnemetats e hdTrowyek circuit
tsum eb dedecerp yb a lebal taht seman eht .tiucric sA htiw lla ,slebal eht lebal noeht
circuit t nte sm uet mtodane tdes eby cb,e sry epndc anataps sudm nhetiw a (noloc :). The
d eor te nted .o rbi sll fdastieoe oep no bchywtno nta tbo soceesltleulhnaalbmoToeoclf
.ecaps yrevE tiucric tsum dne htiw eht endcircuit .tnemetats ehT endcircuit drowyek
.ec a eptnsso adyteebaldec etersbpum
ehT inputs dna outputs stnemetats enifed eht yramirp stupni dna stuptuo fo a.tiucric
ehT inputs dna outputs s d tr soduwe myde eebykcber p ttas a.eeen lcoganpi sewhotlloF
drowy eski a tsil fyo rsatmuiprnp i rsotupt ufoo .ethitucri c eyh rTsatmuipr npeiraesoht
s t eutvpai n hewistcee enunrleah vwuo yepyt a w ,etrnuo ptdncni esa yvteruhaptmtiurop
era esoht stuptuo taht era deyalpsid ni eht Simulation Trace .wodni w e hsTtsi lfsotupni
dna stuptuo era stsil fo se mdaentarapes yb .sammoc erehT dluohs eb on secaps nieseht
.stsil hcaE yramirp tupni dluohs raeppa sa na tupni ot ta tsael eno .etag hcaEyramirp
output should be the output of a gate.
d, e gswhy nnotby,iil i ll kgl.w aayleeaeoetlabtebfpntuaapy ecslgstmiu ereetthtaSTatgs
rae plp laliew bea tl ea,hget t easnhgrito r ererera e,fhrite v.ey wroaHssece nlsneiu beahlt
ni eht rorre .egassem tuohtiW siht ,noitamrofni eht rorre segassem yam eb drahot
.esong aid eh Tet aegp ytts udm eded ebedwcno ealyrlbpof t atsa ee.lneocagpns iwolloF
e ehett pa. ygssteis e d haes tt st es snnyousht yieialptTufrlr mcnupoaaenipnmpbeniiirp
ro lanretni .snoitcennoc eeS( retal stnemirepxe rof lanretni ).snoitcennoc fI eht tsilfo
.detti m eoyb asmesehtner aep h,tme teilgn isasniatn osctupni
gniwol leohFt tsil fo stupni si a ammoc dna a tsil fo sdteunpitau to.ns oencsiehtne rapfI
eht tsil fo stuptuo sniatnoc a elgnis ,meti sa si netfo eht ,esac eht sesehtnerap yameb
.dettimo ehT smeti ni eht tupni dna tuptuo stsil tsum eb detarapes yb .sammoc erehT
:gniwoll oe fhfe toney obaemp ye.tt sanGoitacifice ptsuptuo/tup nnsiieca poedsnbluohs
and, or, not, xor, nand, nor, buff, xnor d.e r c nesuli tedl aro i elurwwLbtteDanNHeiFf
.stnemirepxe
3
Experiment 2: Properties of Functions
Experiment 2
The Properties of Boolean Functions
Objective: emirepxE sywrfaa ol tseysn n mf eef ofoiotmoeiosrtaehtegltaverugi ftnnoecre fhtftniidw
.arbeg lnAaelooB
Instructions.arbeg lnA:aelo o fBsow allatnemadn uef httneserp esrnoitau qgeniwoll oef hT
Equation Law
a=1•a Andw ayLtitne dI
a=0+a Orw ayLtitne dI
b=a ab fyotivitatummoC and
a b=+ a+b fyotivitatummoC or
( )cc )b=b(aa f oytivitaicossA and
( a c+ )=(b++a )c+b f oytivitaicossA or
a( ) c=+b ca+ba And r esveotubirt sid or
a c b=+( ()b+a )c+a Or r esveotubirt sid and
0=’aa Andwa lesrevn i
1=’a+a Orwa lesrevn i
esehT swal nac eb y ldleaitfnier megivnriespuxe eht LDHFrotalumis . oT od ,sihttsrif
yef hilh trlc,eiinvwhowitpir ctsieu dcgrniicw o en,leperlhyhoottttfa l tuLermDhaiHttsFs
.w ayltitne dDINA
AndIdentity: circuit
inputs a
outputs q
one c1
g1: and (a,c1),q
endcircuit
tupnI eht owt srotcev 0 dna ,1 dna esu eht noitalumis ecart ot yfirev taht eht tupnidna
output are the same. Now create a new Circuit Description g wn oied thnyctibewles New
dnammoc morf eht File ,unem dna raelc eht Simulation Window yb gnitceles eht Clear
Tr mdeonhrat fmemcoac Edit to i te u.nhwgcuitenrnniie wcmne oepelhyhlTttof Circuit
Description.wod niw
4
Experiment 2: Properties of Functions
AndAssoc: circuit
inputs a,b,c
outputs left,right
left1: and (a,b),x1
left2: and (x1,c),left
right1: and (b,c),x2
right2: and (a,x2),right
endcircuit
tupnI eht l leucfneuqe sfo t h,gsireotce vsa det s,iwloleb dna tnirp htob eh ttiucri cdnaeht
.eca rntoitalumis
0,0,0 1,0,0
0,0,1 1,0,1
0,1,0 1,1,0
0,1,1 1,1,1
.evo bdaets islw aelv irfeh teo hhtt itwnemirep xsei httaepeR
.stlus ee rhtt n.i ervPitaicos sd aneavitatumm ohct os)biRO Xre(ovisulc xtea hytfireV
.stlus ee rht tn.i ervPitaicos st aot nuebvitatumm osDciN AtNa hytfireV
.stlus ee rht tn.i ervPitaicos st aot nuebvitatumm osR ciOtNa hytfireV
Results: nruT ni eht detn itrupptuo rof hc a.etiucric ehT tiucric dna eht ecar tdluo hrsaeppa noeht
.eg aepmas
A x 1
FHDL: oT etelpmoc siht tnemirepxe ti siyrassecen
B
ot retsam eht tra fo gnimrofsnart anaelooB
L e f t
noitauqe otni na LDHF ,noitpircsed dnayb
noo tiknt r ia. oacsfwieotltep anmgi teshrTif C
elpmaxe setartsulli woh ot eralcedtnatsnoc
.slangis ehT one tnemetats seralcedslangis
ot eb tnatsnoc ,eno elihw eht zero tnemetats
R i g h t
seralced slangis ot eb tnatsnoc .orez esehT
owt stnemetats evah eht emas tamrof saeht
inputs dna outputs .stnemetats ehTdnoces
x 2
elpmaxe swohs woh ot eralced dna esu
lan r.estlnaingis nI sih t,elpmaxe eht slangis
Logic diagram for AndAssoc
x1 dna x2 era lanretni .slangis nAlanretni
langis tsum raeppa sa eht tuptuo fo eno ,etag dna eht tupni fo eno ro mor other gates.
tfnoelavi uL qDet eHhaeFthttoN a’.tnemeta tgsniwoll oef h sti
gaprime: not a,aprime
5
Experiment 3: Theorems
Experiment 3
Theorems and Canonical Forms
Objective: t nseimh iTlrleip wxwEolla uoy toscttuirutcsrn ioocct yfir eevmos fo eht csimsearboeht
fo nae l.oaorBbeglA tI lliw osla evig uoy e meocsneire phxteiw eh tlacino nsamcrofrof
.stup no iwnta hetr ohmt iswet aLgD HsFecudort ntinemirep xs.ei shnToitcn unfaelooB
Instructions: ehT gniwollof snoitauqe tneserper emos fo eht erom tnatropmi smeroeht fonaelooB
.arbeglA
Equation Theorem
( ’=)ba ’b+’a sw asL’nagromeD
( a ’=)b+ ’b’a sw asL’nagromeD
a a +=a ycnetopmedI
a a=a ycnetopmedI
( ’=)a’a lovnI noitu
1+a =1 noitprosbA
0 •=a0 noitprosbA
a b=aa+ noitprosbA
a( ) b=+aa noitprosbA
tcurtsn osCtiucric ot yfirev hcae fo eseht .swal tnirP eht tiucric dna noitalumis ecartrof
.hcae
ehT gniwollof elbat stsil eht elbisso psmretnim dna smretxam rof a tupni-eernhatelooB
.noitcnuf
Input Combination Minterm Maxterm
0,0,0 a’b’c’ a+b+c
0,0,1 a’b’c a+b+c’
0,1,0 a’bc’ a+b’+c
0,1,1 a’bc a+b’+c’
1,0,0 ab’c’ a’+b+c
1,0,1 ab’c a’+b+c’
1,1,0 abc’ a’+b’+c
1,1,1 abc a’+b’+c’
tcurtsnoC stiucric rof eht smretnim dna smretxam taht dnopserroc ot eht tupni
snoitanibm o,c0,1,0 dna .0,1,1 etalumiS hcae fo eseht ruof stiucric gnisu lla thgietupni
.hc are oefca rntoitalum ids ntaiucr iec httn i. rsPnoitanibmoc
6
Experiment 3: Theorems
ehT gniwollof elbat sevig eht hturt elbat rof eeht naelooB .snoitcnuf tcurtsnoCowt
stiucric rof hcae ,noitcnuf eno taht si a mus fo ,smretnim dna eno taht si a tcudorpfo
.hc are oefca rntoitalum ids ntaiucr iec httn i. rsPmretxam
Input Combination Function 1 Function 2 Function 3
0,0,0 0 0 1
0,0,1 1 0 0
0,1,0 0 0 1
0,1,1 0 1 1
1,0,0 1 0 0
1,0,1 0 1 1
1,1,0 0 1 1
1,1,1 1 1 0
egshnnTiowiotlc lneourffa d eetrao c m.inylarphamtsoscece n ecud eesRsneohittcnuoft
eht muminim rebmun fo ,slaretil gnisu eht smeroeht detsil ,evoba dna eht cisabswal
debircsed ni tnemirepxE .2 ecnO uoy evah decuder eseht ,snoitcnuf tcurtsnocowt
,gsntiidu nceor npiooscterr o ,eclnhaotniit ga diugnrqnaoeid neo npoosterr oechdtecuder
.em aes het ryae htta hytfir e ovstnoitanibm otcup nli lgani shuc aeetalu m. inSoitauqe
ab+ab’
(a+b)(a+b’)
abc+a’b+abc’
Results:.hc a feeoca rntoitalum ihast igwno l,astiucr ilc l fasotuotni r npniruT
FHDL: oT etelpmoc siht ,tnemirepxe ti si yrassecen ot esu LDHF setag htiw erom nahtowt
.stupni setaG fo epyt and, or, nand, nor, xor , dna xnor rn yeaerbcvamfa ruohntnaibra
.stupni tA tsael ow tstup n ,iedreari utqueb rereht si on re p.ptuimil gni tnneehmWelpmi
setag ,neir aewrderhath er as tdiemsio lp,my igynoboli ottnau htbecnheettLmDeHlFpmi
.set atgup neilpitl u fmsoelpma xeem oes rganiwoll o ef. heTn osnesopmi
g1: and (a,b,c),q1
g2: or (a,b,c,d,e,f,g),q2
g3: nand (a,b,c,d),q3
g4: xor (a,b,c),q4
7
Experiment 4: Two-Level Functions
Experiment 4
Two-Level Functions
Objective:ecudor tl nltiinwemire psxiehT uoy ot eh ttpecnoc fl oe ,vnseanleo-lioot wocdtBnnuafeht
.snoitcnu fhcu sgnizimini mro fseuqinhcet
Instructions: se, ,ttsg eiam nrod luereiowngb c renwftanaereCtoo ithinnldtstcoileaumozh fitsmiinim
ot te shretelblmaum ns.fsot neam cisirt lp cp.ummdiroor fpe-sfU o-mus esU haguanraK
.snoitanibmo ctupn ithgi ell agnis usnoitcnu fhto betalum i .Snoitcnu feh tezimini mo tpam
Input Value Input Value
0,0,0 0 1,0,0 0
0,0,1 0 1,0,1 1
0,1,0 1 1,1,0 0
0,1,1 1 1,1,1 1
eziminiM eht gniwo lnlooiftcnuf gnisu a hguanraK .pam tnemelpmI eht noitcnuf sana
LDHF ,tiucric dna etalumis ti gnisu lla tupni snoitanibmoc ot evorp ruoydeziminim
.tce r nrsooiictcnuf
F(a,b,c,d) = SS (0,2,3,4,11,12)
sserpxE eht gniwollof noitcnuf sa a tcudorp fo .smretxam tnemelpmI eht noitcnufni
LDHF dna etalumis ti gnisu lla thgie tupni .snoitanibmoc eziminiM eht noitcnufotni
smus-fo-tcudorp mrof gnisu a hguanraK .pam tnemelpmI eht deziminim noitcnufni
.snoitanibmo ctupn ithgi ell agnis ut ietalumi sdn aLDHF
Input Value Input Value
0,0,0 0 1,0,0 0
0,0,1 0 1,0,1 1
0,1,0 0 1,1,0 1
0,1,1 1 1,1,1 0
eziminiM eh tgn iswnooliltocf ngunfisu eht t’nod erac .snoitidnoc tnemelpmI htobeht
lanigiro dna eht deziminim snoitcnuf ni ,LDHF dna etalumis meht htiw lla tupni
snoi toatn iwbom h oy s,cetlhpa tece cirrxtaoenfe de ih tt.’sneorDaC h geussaUpnarmaK
.noitazimini meh trof
F(a,b,c,d) = a’bc’d’ + a’b’c’d + a’b’cd + a’bcd + abcd “ ab’cd
DontCare(a,b,c,d) = a’b’c’d’ + a’bc’d + a’bcd’
F(a,b,c) = a’b’c’ + ab’c + a’bc
DontCare(a,b,c) = ab’c’ + abc
8