Parity

CircuitOdd-Parity Circuit

（奇校驗電路）Output

is

1

if

an

odd

number

of

its

inputs

are

1.(如果輸入有奇數個1，則輸出為1)Even-Parity

Circuit（偶校驗電路）Output

is

1

if

an

even

number

of

its

inputs

are1.(如果輸入有偶數個1，則輸出為1)What

is

the

use

of

Parity

?Can

detect

dataerror.Parity

CircuitHow

torealize

Parity

?Use

XOR

orXN

atesExample

for

Odd-ParitySend

data:

1

1

0

1

0

0

1

1Valid

Data

Parity

Bit,to

ensure

the

totalnumber

of

1

isodd.Received

data:

1

1

0

1

0

0

1

1The

total

number

of

1is

odd,

Data

is

correct

!Received

data:

1

0

0

1

0

0

1

1The

total

number

of

1

is

even,

Data

is

wrong!For

Dhecking,

Parity

is

not

reliable

but

very

simple.XOR

and

XNatesParity

CircuitF

=

X

Y

=

X·Y’

+

X’·YTrue

TableF

=

X

Y=

X·Y’

+

X’·Y=

X·(X’+Y’)

+

Y·(X’+Y’)=

X·(X·Y)’

+

Y·(X·Y)’XOR

and

XNatesParity

CircuitAB=

(AB’)’Any

two

signals(inputs

or

output)

of

an

XORorXN ate

may

be

complementedwithout

changing

the

resulting

logic

function.(對于異或門、同或門的任何2個信號(輸入或輸出)可以取反，而不改變結果)Refer

toFigure

6-69=

A’B’

=

(A’B)’A⊙B

=

A’⊙B’=

A’B

=

AB’Parity

CircuitsParity

Circuit1

變量為1

的個數是奇數0

變量為1

的個數是偶數1

變量為0

的個數是偶數0

變量為0

的個數是奇數奇校驗的輸出反相就得到偶校驗若輸入變量中1的個數為奇數，則

0的個數為偶數？0的個數為奇數？檢測1的個數用異或運算A0

A1

…

An

=檢測0的個數用同或運算A0⊙A1⊙

…

⊙An

=Parity

CircuitsParity

CircuitI1I2I3I4INODDI1I2I3I4IMINODDTree

Structure(樹狀連接)Cascading

XatesDaisy-Chain

Connection(菊花鏈式連接)The

74x280

9-Bit

Parity

GeneratorParity

CircuitWhy

9

bits

?Inorder

toverify

onebyteParity-Checking

ApplicationsParity

CircuitAEVENODD74x280HIAEVENODD74x280HIERROR發端始終有偶數個1收端ODD有效表示出錯發端收端用于檢測數據在傳輸和 過程中是否出現差錯DB[0:7]

DB[0:7]Parity-Checking

ApplicationsParity

CircuitAEVENODD74x280HIAEVENODD74x280HI發端始終有奇數個1收端EVEN有效表示出錯ERROR發端收端用于檢測代碼在傳輸和 過程中是否出現差錯DB[0:7]

DB[0:7]VccParity-Checking

ApplicationsParity

Circuit=1=0=0=0=1=0=1=0=0PFigure6-72Parity-Checking

ApplicationsParity

CircuitFigure

6-72=1=0=1=0=0=1=1PPComparatorsCompare

two

Binary

words

and

indicate

whether

they

are

equal(比較2個二進制數值并指示其是否相等的電路

)(Equality)

Comparator

:

Check

if

two

Binary

words

are

equal(等值比較器：檢驗兩個二進制數值是否相等)Magnitude

Comparator

:

Compare

their

magnitude(數值比較器：比較數值的大小>,=,<)ComparatorsHow

tobuild

a

1-bit

Comparator

?Use

XOR

or

XNORAB

DIFFABEQDIFF

:differentEQ

:

equalComparator

StructureComparatorsHow

to

build

a

n-bit

Comparator

?Comparator

StructureDIFFA0B0A1B1A2B2A3B3Compare

each

pair

of

bits.——

Parallel

Comparator——

Serial

ComparatorComparatorsHow

to

build

a

n-bit

Comparator

?Comparator

Structure若給足夠的異或門和寬度足夠的或門，可以搭建任意輸入位數的等值比較器。Compare

each

pair

of

bits.——

Parallel

Comparator——

Serial

Comparator0110

=0111

?ComparatorsHow

to

build

a

n-bit

Comparator

?Comparator

StructureCompare

each

pair

of

bits.——

Parallel

Comparator——

Serial

ComparatorAnd

how

to

compare

seriallyCan

use

Iterative

Circuit.ComparatorsIterative

CircuitsComparatorsIterative

ComparatorX0

Y0X

YCMPEQI

EQOEQ1EQ2EQNEQN-11X1

Y1X

YCMPEQI

EQOXN-1

YN-1X

YCMPEQI

EQO——每位串行比較EQOABEQI用于級聯的輸入Why?EQN

=

(XN-1⊙

YN-1)

*

(XN-2⊙

YN-2)

*...

*(X0

⊙

Y0)

*

1迭代的方法節省一點器件成本，但速度慢ComparatorsMagnitude

Comparator1-Bit

MagnitudeComparator①A>B（A=1,B=0）則

A·B’=1

可作為輸出信號②A<B（A=0,B=1）則

A’·B=1

可作為輸出信號③A=B

，則AB=0，可作為輸出信號輸出低電平有效EQ_L

=

((A’·B)’

·

(A·B’)’)’=A’·B+A·B’

=

AB

=

(A⊙B)’LT

:

Less

ThanEQ

:

EqualGT

:

Greater

ThanABLT_LEQ_LGT_L(A’·B)’(A·B’)’ComparatorsMagnitude

Comparatorn-Bit

Magnitude

ComparatorA(A3A2A1A0)和B(B3B2B1B0)自高而低逐位比較

EQ=(A3⊙B3)·(A2⊙B2)·(A1⊙B1)·(A0⊙B0)LT=EQ’·GT’=(EQ+GT)’

——節約成本(A3(A3GT

=

(A3·

B3’)B3)·

(A2·

B2’)?(A3

⊙B3)·(A

2

⊙B2)·

(A1·

B1’)?B3)·(A

2

⊙B2)·(A

1

⊙B1)·

(

A0·

B0’)+++ComparatorsStandard

MSI

Magnitude

ComparatorsALTBINAEQBINAGTBINALTBOUT=

(A<B)

+

(A=B)·ALTBIN4-Bit

Comparator74x85級聯輸入，用于擴展通常低位74x85的輸出接74x85的輸入A

>BA

=B &

A

>B低位 低位A>BA=B：低位和

都相等AEQBOUT

=

(A=B)·AEQBINAGTBOUT=

(A>B)+

(A=B)·AGTBINComparatorsXD[11:0]YD[11:0][3:0][7:4][11:8]X<YX=YX>Y+5VA<BOA=BOA>BOA<BIA=BIA>BIA0~A3B0~B3A<BOA=BOA>BOA<BIA=BIA>BIA0~A3B0~B3A<BOA=BOA>BOA<BIA=BIA>BIA0~A3B0~B3Serial

Expanding

Comparators3片74x85構成12位比較器低位74x85

74x85

74x85Why?Standard

MSI

Magnitude

ComparatorsComparators8位比較器74x682問題1：怎樣表示以下輸出？高電平有效：P

NE

Q高電平有效：P

E高電平有效：P

GE

Q高電平有效：P

LT

Q......Standard

MSI

Magnitude

ComparatorsComparators問題2：能否擴展？——Paralel

Expanding

Comparators3片74x682構成24位比較器P0~P7

P=QQ0~Q7

P>QP0~P7

P=QQ0~Q7

P>QP0~P7

P=QQ0~Q7

P>Q[7:0][15:8][23:16]Q[23:0]

P[23:0]PEPGTQStandard

MSI

Magnitude

Comparators8位比較器74x682ComparatorsStandard

MSI

Magnitude

ComparatorsExample

1Design

a

combinational

component

that

ouput