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Combinatorial Logic Design Multiplexers and ALUs CS 64: Computer Organization and Design Logic Lecture #14 Ziad Matni Dept. of Computer Science, UCSB

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Page 1: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

CombinatorialLogicDesignMultiplexersandALUs

CS64:ComputerOrganizationandDesignLogicLecture#14

ZiadMatni

Dept.ofComputerScience,UCSB

Page 2: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Administrative

•  Remainingonthecalendar…Thissupersedesanythingonthesyllabus

2

DATE TOPIC ASSIGNMENTS

Thu.3/1 SimplifyingDigitalLogicFunctions Lab6(dueFri.3/2)

Tue.3/6 CombinatorialLogic

Thu.3/8 SequentialLogic Lab7(dueFri.3/9)

Tue.3/13 FiniteStateMachines

Thu.3/15 Ethics Labs8and9(dueFri.3/16)

Page 3: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

LectureOutline

•  CombinatorialLogic

•  SelectionusingMultiplexers

•  BasicALUDesign

3/6/18 Matni,CS64,Wi18 3

Page 4: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Exercise2

•  Giventhefollowingtruthtable,drawtheresultinglogiccircuit

3/6/18 Matni,CS64,Wi18 4

A B C F0 0 0 10 0 1 10 1 0 10 1 1 01 0 0 11 0 1 11 1 0 01 1 1 0

00 01 11 10

0

1

ABC

111

F(A,B,C)=B’+A’.C’

1 1

B

AC

F

Page 5: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Exercise3

•  Giventhefollowingschematicofacircuit,(a)writethefunctionand(b)filloutthetruthtable:

X=A.B+(A.C)’(notethatalsomeans:X=A.B+A’+C’)

3/6/18 Matni,CS64,Wi18 5

ABAC

X

A.B

(A.C)’

A B C X0 0 0 10 0 1 10 1 0 10 1 1 11 0 0 11 0 1 01 1 0 11 1 1 1

X

Page 6: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Exercise3

•  Giventhefollowingschematicofacircuit,(a)writethefunctionand(b)filloutthetruthtable:

X=A.B+(A.C)’(notethatalsomeans:X=A.B+A’+C’)

3/6/18 Matni,CS64,Wi18 6

ABAC

X

A.B

(A.C)’

A B C X0 0 0 10 0 1 10 1 0 10 1 1 11 0 0 11 0 1 01 1 0 11 1 1 1

Page 7: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

3/6/18 Matni,CS64,Wi18 7

Page 8: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Multiplexer(Muxforshort)

•  Typicallyhas3groupsofinputsand1output–  IN:2data,1select–  OUT:1data

•  1oftheinputdatalinesgetsselectedtobecometheoutput,basedonthe3rd(select)input–  If“Sel”=0,thenI0getstobetheoutput–  If“Sel”=1,thenI1getstobetheoutput

•  TheoppositeofaMuxiscalledaDemulitplexer(orDemux)

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Page 9: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

MuxConfigurations

3/6/18 Matni,CS64,Wi18 9

MuxescanhaveI/Othataremultiplebits

Ortheycanhavemorethantwodatainputs

2:1

A0A1B0B1SEL

O0O1

Thisiscalleda2-bit,2-to-1mux

6:1

ABCDEFSEL

O

Thisiscalleda1-bit,6-to-1mux

Page 10: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

TheUseofMultiplexers

•  Makesitpossibleforseveralsignals(variables)toshareoneresource– Verycommonlyusedindatacommunicationlines

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Mux De

mux

… …DataLines

DataLines

Select

Shareddataline(“trunk”)

Page 11: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

MuxTruthTableandLogicCircuit1-bitMux

I0 I1 S O0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

3/6/18 Matni,CS64,Wi18 11

00 01 11 10

0

1

I0I1S

1

11

1

O=S.I1+S’.I0

I0I1

S

O

=linesarephysicallyconnected

00011011

Page 12: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Beyond1-bitMuxes•  Generalmuxform:N-bit,M-to-1•  Where: N=howwidethedatabusis(inbits,min.1)

M=howmanyinputstothemux(min.2)

•  The“select”input(S)hastobeabletoselect 1outofMinputs–  So,ifM=2,Sshouldbeatleast1bit(S=0foroneline,S=1fortheother)–  ButifM=3,Sshouldbeatleast2bits(why?)–  IfM=4,Sshouldbeatleast???

•  Atleast2bits–  IfM=5,Swillhavetobe???

•  Atleast3bits

3/6/18 Matni,CS64,Wi18 12

...

S

Minputs

Page 13: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

WhatDoesThisCircuitDo?

3/6/18 Matni,CS64,Wi18 13

101010(akasynchronousclock)

01S

a0a1a2a3a4a5

b0b1b2b3b4b5

time

time

a0 a1 a2 a3 a4 a5

1 0 1 0 1 0

b0 a1 b2 a3 b4 a5

b0 b1 b2 b3 b4 b5

b0a1b2a3b4a5

Page 14: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

WhatDoesThisCircuitDo?

3/6/18 Matni,CS64,Wi18 14

S0

AB 0

1S

01S

RCo

RCo

S0

1bAdder

1bAdder

01

01S

S1

F

I0I1Ci

I0I1Ci

Page 15: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

3/6/18 Matni,CS64,Wi18 15

S0

AB 0

1S

01S

RCo

I0I1Ci

RCo

S0

1bAdder

1bAdder

01

01S

S1 S0F0 0 A&&B0 1 A||B1 0 A+B1 1 A–B

S1

F

Forsimplicity,theCarryOutandOverflowbitsarenotshown

I0I1Ci

WhatDoesThisCircuitDo?

Page 16: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

SimulationofCombinatorialLogic

•  Goto:https://logic.ly/demo/

IN-CLASSDEMONSTRATION

(NeededforLab#7)3/6/18 Matni,CS64,Wi18 16

Page 17: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Arithmetic-LogicUnit(ALU)

•  Recall:theALUdoesallthecomputationsnecessaryinaCPU

•  ThepreviouscircuitwasasimplifiedALU:– WhenS=00,R=A+B– WhenS=01,R=A–B– WhenS=10,R=AANDB– WhenS=11,R=AORB

3/6/18 Matni,CS64,Wi18 17

Page 18: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

SimplifiedALU

•  Wecanstring1-bitALUstogethertomakebigger-bitALUs(e.g.32bALU)

3/6/18 Matni,CS64,Wi18 18

1bitALU

…

A31B31S

R0 R1 R2 R3 R31

1bitALU

Co

RABS

Ci

1bitALU

1bitALU

1bitALU

1bitALU

A0B0S A1B1S A2B2S A3B3S

CoCi

Page 19: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

AbstractSchematicoftheMIPSCPU

3/6/18 Matni,CS64,Wi18 19

Page 20: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

Combinatorialvs.SequentialLogic

•  TheCPUschematicshows bothcombinatorialandsequentiallogicblocks

•  CombinatorialLogic–  Combiningmultiplelogicblocks–  Theoutputisafunctiononlyofthepresentinputs–  Thereisnomemoryofpast“states”

•  SequentialLogic–  Combiningmultiplelogicblocks–  Theoutputisafunctionofboththepresentinputsandpastinputs–  Thereexistsamemoryofpast“states”

3/6/18 Matni,CS64,Wi18 20

Page 21: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

YourTo-Dos

•  Lab7willbedueonFriday,3/9– WewilltakeattendanceforthislabonThursday

•  Lab8willbedueonFriday,3/16–  I’llissueitthisweek,butyouhavemoretimeforit– WillcontaininfofromnextMonday’slecture

•  Reminder:there’saLab9aswell!– Online“quiz”ontheEthicslesson,dueFri.3/16

3/6/18 Matni,CS64,Wi18 21

Page 22: Combinatorial Logic Design Multiplexers and ALUs · Combinatorial vs. Sequential Logic • The CPU schematic shows both combinatorial and sequential logic blocks • Combinatorial

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