16/07/2015CSE1303 Part B lecture notes 1 Hardware Implementation Lecture B17 Lecture notes section B17

04/19/23 CSE1303 Part B lecture notes 1

Hardware Hardware ImplementationImplementation

Lecture B1Lecture B177

Lecture notes section B1Lecture notes section B177


Last timeLast time

Analysis of translationAnalysis of translation Writing efficient CWriting efficient C


In this lectureIn this lecture

GatesGates Combinatorial logicCombinatorial logic

adderadder ALUALU

Sequential logicSequential logic flip-flopflip-flop memorymemory

CPUCPU fetch-decode-execute cyclefetch-decode-execute cycle


How to make a computerHow to make a computer

Computers are electronic Computers are electronic equipmentequipment contain many connected electronic contain many connected electronic

componentscomponents• memorymemory• Central Processing Unit (Central Processing Unit (CPUCPU))• specialized devices (network, video, etc.)specialized devices (network, video, etc.)

components largely made of circuits components largely made of circuits containing wires and containing wires and gatesgates


GatesGates

Tiny electronic switchesTiny electronic switches made of transistorsmade of transistors implement implement Boolean logicBoolean logic

• 0/1 0/1 low/high voltage low/high voltage• digitaldigital

for given inputs, produce known for given inputs, produce known outputoutput• according to according to truth tabletruth table

represented in circuit diagrams by represented in circuit diagrams by symbolssymbols


GatesGatesNOTNOT

In 1In 1 In 2In 2 OutOut

00 00 00

00 11 00

11 00 00

11 11 11

InIn OutOut

00 11

11 00

ANDAND


00 00 00

00 11 11

11 00 11

11 11 11

OROR


00 00 00

00 11 11

11 00 11

11 11 00

XORXOR


Combinatorial logicCombinatorial logic

What about more complex truth What about more complex truth tables?tables?

Made by Made by combiningcombining many gates many gates togethertogether wires connect inputs and outputswires connect inputs and outputs each wire can carry only one bit, 0 or each wire can carry only one bit, 0 or

11



Circuits made from collections of Circuits made from collections of gatesgates outputs depend only on inputsoutputs depend only on inputs

• not on prior statenot on prior state

characterized by truth tablecharacterized by truth table comparable to Boolean expressioncomparable to Boolean expression



X = (A & ~B) | (B & C)X = (A & ~B) | (B & C)

AA BB CC XX

00 00 00 00

00 00 11 00

00 11 00 00

00 11 11 11

11 00 00 11

11 00 11 11

11 11 00 00

11 11 11 11

AA

BB

CC

XX

all three of formsall three of formsare equivalent; each can are equivalent; each can be converted to the other be converted to the other

two.two.

00

11

11

00

00

00

11

1111

11

00

11

boolean boolean expressionexpression

logic circuitlogic circuit truth tabletruth table



Many parts of a computer are Many parts of a computer are constructed of combinatorial logicconstructed of combinatorial logic adderadder circuit circuit

• performs additionperforms addition

arithmetic logic unit (arithmetic logic unit (ALUALU))• performs many kinds of arithmetic and performs many kinds of arithmetic and

bitwise logical operationsbitwise logical operations• contains adder circuitcontains adder circuit

multiplexer and decodermultiplexer and decoder• direct bit traffic between componentsdirect bit traffic between components


AdderAdder

A combinatorial circuit that adds A combinatorial circuit that adds binary valuesbinary values according to this truth tableaccording to this truth table

In 1In 1 In 2In 2 SumSum CarryCarry

00 00 00 00

00 11 11 00

11 00 11 00

11 11 00 11

Sum is equivalent Sum is equivalent to XORto XOR

Carry is Carry is equivalent to equivalent to

ANDAND


AdderAdder

In 1In 1

In 2In 2

CarryCarry

SumSum

This circuit can add two binary digits This circuit can add two binary digits and is called a and is called a half-adderhalf-adder


AdderAdder

55

33

33

88

11

44++

11

11

Why “half-Why “half-adder”. . . ?adder”. . . ?

. . . because to add . . . because to add multi-digit numbers multi-digit numbers

each column requires each column requires twotwo additions additions

99


Full adderFull adder

in 1in 1in 2in 2

sumsum

carry carry outout

carry carry inin half half

addersadders

This circuit is called This circuit is called a a full adderfull adder and can and can

add three binary add three binary digitsdigits

This OR gate This OR gate combines the combines the carries from carries from the two half-the two half-

addersadders


Ripple-carry adderRipple-carry adderA0A0

out3out3 out2out2 out1out1 out0out0

B0B0A1A1

B1B1A2A2

B2B2A3A3

B3B3


Ripple-carry adderRipple-carry adderA0A0

out3out3 out2out2 out1out1 out0out0

B0B0A1A1

B1B1A2A2

B2B2A3A3

B3B311

0000

1111

1100

00

01010101 + + 01100110 = = 10111011

11110011

00001100

110000

00

00

00

11

00

00


Ripple-carry adderRipple-carry adder

So named because gate results So named because gate results (including carries) propagate (including carries) propagate (“ripple”) from LSB to MSB(“ripple”) from LSB to MSB right to leftright to left corresponds to how humans add corresponds to how humans add

numbers with pen and papernumbers with pen and paper More sophisticated, faster, adder More sophisticated, faster, adder

circuits exist that can create the circuits exist that can create the higher order carries more quicklyhigher order carries more quickly


AdderAdder

++

Adders (and other Adders (and other arithmetic arithmetic

circuits) are circuits) are usually drawn like usually drawn like

this in block this in block diagramsdiagrams

A3-A0A3-A0 B3-B0B3-B0

out3-out0out3-out0

inputsinputs

outputoutputcollections of parallel, collections of parallel,

related wires like this are related wires like this are known as known as busesbuses; they carry ; they carry

multi-bit values between multi-bit values between componentscomponents


ArithmeticArithmetic

Computers need to do more than Computers need to do more than just additionjust addition arithmetic: arithmetic: + – * / %+ – * / % logic: logic: & | ~ << >>& | ~ << >>

Need a circuit that can Need a circuit that can selectselect operation to performoperation to perform


Arithmetic Logic Unit Arithmetic Logic Unit (ALU)(ALU)

++ ** && <<<< . . .. . .

MUXMUX

op op 00

op op 11

op op 22

op op 33

opop

outout

AA BB

MultiplexerMultiplexer: a : a combinatorial combinatorial circuit which circuit which

selects selects exactly one exactly one

inputinput

op selects operation:op selects operation:

0 = add, 1 = 0 = add, 1 = multiply, ...multiply, ...

more more operations operations

herehere

00 11 22 33 ....


Arithmetic Logic Unit Arithmetic Logic Unit (ALU)(ALU)

++ ** && <<<< . . .. . .

MUXMUX

op op 00

op op 11

op op 22

op op 33

op = 3op = 3

out = 60out = 60

A = 15A = 15 B = 2B = 2

other results other results also computed also computed but ignored by but ignored by

multiplexermultiplexer

more more operations operations

herehere

for for example: example: compute compute 15 << 215 << 2

00 11 22 33 ....


MemoryMemory

Computers need memory for storageComputers need memory for storage Different kinds of memory distinguished Different kinds of memory distinguished

by speed, size, cost and proximity to CPUby speed, size, cost and proximity to CPU main memorymain memory

• slowish, huge, cheap, far from CPUslowish, huge, cheap, far from CPU• typical size 10typical size 1099 bits bits

cachecache• fast, medium-sized, expensive, near to CPUfast, medium-sized, expensive, near to CPU• typical size 10typical size 1066 bits bits

registersregisters• extremely fast, tiny, very expensive, located on extremely fast, tiny, very expensive, located on

CPUCPU• in MIPS (32 GPRs)×32 bits = 1024 bitsin MIPS (32 GPRs)×32 bits = 1024 bits


MemoryMemory

The The smallestsmallest piece of memory is a piece of memory is a single binary digit (single binary digit (bitbit)) can hold can hold 0 or 10 or 1 only only

A one-bit memory is called a A one-bit memory is called a flip-flip-flopflop or a data or a data latchlatch because its value can flip and flop because its value can flip and flop

between 0 and 1between 0 and 1 because it can latch onto a data value because it can latch onto a data value

and store itand store it


Flip-flopFlip-flop

Flip-flop needs two operation modesFlip-flop needs two operation modes writewrite: store (memorize) a value: store (memorize) a value readread: load (recall) a previously stored value: load (recall) a previously stored value

Also needAlso need data indata in

• for telling flip-flop what value to store (0 or 1)for telling flip-flop what value to store (0 or 1)• used only when writingused only when writing

data outdata out• for finding out what value flip-flop currently contains for finding out what value flip-flop currently contains

(0 or 1)(0 or 1)• used only when readingused only when reading


Flip-flopFlip-flop

Flip-flop can be implemented with Flip-flop can be implemented with gatesgates

Not combinatorial logicNot combinatorial logic because current output may depend because current output may depend

on previous stateon previous state Example of Example of sequential logicsequential logic

current output depends on inputs and current output depends on inputs and prior outputprior output


Flip-flopFlip-flop

read/writeread/write

data indata in

data outdata out

read/write read/write control: 0 = control: 0 =

read, 1 = writeread, 1 = write

NOR gate: OR gate NOR gate: OR gate followed by NOT gatefollowed by NOT gate


Flip-flop: writingFlip-flop: writing

read/write read/write = 1 (write)= 1 (write)

data in = 1data in = 1

data out = data out = 11

11

1111

0000

11

11

00

1100

11

when read/write = when read/write = 1, data out = data 1, data out = data

inin

Try changing data in to Try changing data in to 0 and watch data out0 and watch data out


Flip-flop: readingFlip-flop: reading

read/write read/write = 0 (read)= 0 (read)

data in = ?data in = ?

data out = data out = 11

??

??00

??00

00

00

00

1100

11

when read/write = 0, no signals when read/write = 0, no signals in box can change, data out in box can change, data out

holds value regardless of data holds value regardless of data inin


Flip-flopFlip-flop

DD QQ

CKCK

Flip-flops are often Flip-flops are often drawn like this in drawn like this in block diagramsblock diagrams

D = D = data indata in

Q = Q = data outdata out

CK is read/write (“clock” CK is read/write (“clock” because this input is often because this input is often connected to computer’s connected to computer’s

processor clock)processor clock)


MemoryMemory

Memory can store many bits Memory can store many bits independentlyindependently many flip-flopsmany flip-flops

Need to identify which bit (flip-flop) Need to identify which bit (flip-flop) to read or writeto read or write

Give each flip-flop a unique Give each flip-flop a unique number (number (addressaddress))


MemoryMemory

DD

CKCK

QQ

DD

CKCK

QQ

DD

CKCK

QQ

DD

CKCK

QQ

00

11

22

33

......

00

11

22

33

......

. . . millions more flip-flops . . .. . . millions more flip-flops . . .

MU

XM

UX

DE

CD

EC

address 0address 0

address 1address 1

address 2address 2

address 3address 3

data indata in

addressaddress

rd/wrrd/wrdata data outout

Decoder: feeds input to selected output, 0 to all Decoder: feeds input to selected output, 0 to all othersothers


Memory: writingMemory: writing

DD

CKCK

QQ

DD

CKCK

QQ

DD

CKCK

QQ

DD

CKCK

QQ

00

11

22

33

......

00

11

22

33

......


MU

XM

UX

DE

CD

EC

address 0address 0

address 1address 1

address 2address 2

address 3address 3

data indata in

addressaddress


00

22

11

Writing value Writing value 1 to flip-flop 1 to flip-flop at address 2at address 2

1111

00

00

11

??

??

11

??


Memory: readingMemory: reading

DD

CKCK

QQ

DD

CKCK

QQ

DD

CKCK

QQ

DD

CKCK

QQ

00

11

22

33

......

00

11

22

33

......


MU

XM

UX

DE

CD

EC

address 0address 0

address 1address 1

address 2address 2

address 3address 3

data indata in

addressaddress


00

22

Reading Reading value from value from flip-flop at flip-flop at address 2address 2

1100

00

00

00 11 11


MemoryMemory

Memory usually operates in terms Memory usually operates in terms of bytes (8 bits), not single bitsof bytes (8 bits), not single bits

Repeat memory circuit eight timesRepeat memory circuit eight times connect each memory circuit to one connect each memory circuit to one

of the eight lanes of the data busof the eight lanes of the data bus reads and writes occur in parallel for reads and writes occur in parallel for

each bit in byteeach bit in byte


Central Processing Unit Central Processing Unit (CPU)(CPU)

Coordinates all computer’s components Coordinates all computer’s components according to program being runaccording to program being run

ContainsContains registersregisters ALUALU program counter (program counter (PCPC))

• address of current instructionaddress of current instruction instruction register (instruction register (IRIR))

• copy of current instructioncopy of current instruction control logiccontrol logic

Runs programs using Runs programs using fetch-(decode)-fetch-(decode)-execute cycleexecute cycle


CPUCPU

RegistersRegisters

ALUALU

PCPC

IRIR

MemoryMemoryControlControl

logiclogic

inin

outout

addraddr rd/rd/wrwr


Fetch-execute cycle: fetchFetch-execute cycle: fetch

RegistersRegisters

ALUALU

PCPC

IRIR


logiclogic

inin

outout

addraddr rd/rd/wrwr

Stage 1 of fetch-Stage 1 of fetch-execute cycle: execute cycle: instruction at instruction at

address pointed to address pointed to by PC is fetched by PC is fetched

into IRinto IR


Fetch-execute cycle: Fetch-execute cycle: decodedecode

RegistersRegisters

ALUALU

PCPC

IRIR


logiclogic

inin

outout

addraddr rd/rd/wrwr

Stage 2 of fetch-execute Stage 2 of fetch-execute cycle: instruction (now in cycle: instruction (now in IR) is decoded by control IR) is decoded by control logic to determine which logic to determine which

operation to performoperation to perform


Fetch-execute cycle: Fetch-execute cycle: executeexecute

RegistersRegisters

ALUALU

PCPC

IRIR


logiclogic

inin

outout

addraddr rd/rd/wrwr

Stage 3 of Stage 3 of fetch-execute fetch-execute

cycle: CPU cycle: CPU performs the performs the operation (for operation (for

example, example, arithmetic on arithmetic on two registers)two registers)


Fetch-execute cycle: update Fetch-execute cycle: update PCPC

RegistersRegisters

ALUALU

PCPC

IRIR


logiclogic

inin

outout

addraddr rd/rd/wrwr

Stage 4 of Stage 4 of fetch-execute fetch-execute

cycle: PC’s cycle: PC’s value is value is

updated to updated to point to the point to the

next instructionnext instruction


Covered in this lectureCovered in this lecture

GatesGates Combinatorial logicCombinatorial logic

adderadder ALUALU

Sequential logicSequential logic flip-flopflip-flop memorymemory

CPUCPU fetch-decode-execute cyclefetch-decode-execute cycle


Going furtherGoing further

Digital logicDigital logic CSE1308/CSE2306CSE1308/CSE2306

Next timeNext time RevisionRevision

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16/07/2015CSE1303 Part B lecture notes 1 Hardware Implementation Lecture B17 Lecture notes section B17