北科大853電路理論與自動控制原理電子數(shù)電課件

Basic

Combinational

Logic

Circuits

AnalysisImplementing（

Design

）

Combinational

Logic組合邏輯電路的實現(xiàn)(設計）The

Universal

Property

of

NAND

and

NOR

Gates5-4 Combinational

Logic

Using

NANDand

NOR

Gates5-5 Logic

Circuit

Operation

With

Pulse

Waveform5 Analysis

and

Design

of

Combinational

LogicCHAPTER

OUTLINE組合邏輯電路分析和設計Definition

of

Combinational

LogicLogic

circuits

without

feedback

from

output

to

the

input,

outputsdepend

only

on

current

inputs

(not

on

history).

constructed

from

afunctionally

complete

gate

set,are

said

to

be

combinational5-1 Basic

Combinational

Logic

AnalysisKinds

of

combinational

analysis:exhaustive

(truth

table)algebraic

(expressions)simulation

/

test

benchAND-OR

Logic（與-或邏輯電路）AND-OR-Invert

Logic（與-或-非邏輯電路）Exclusive-OR

Logic（異-或邏輯電路）AND-OR

LogicINPUTSA

B

C

DABCDOUTPUTX0000000000100000100000011011010000001010000110000011101110000001001000101000010110111100101110110111101011111111ABX

X=AB+CDCDFigure5-1

An

example

of

AND-OR

logicTruth

table

for

AND-ORlogic

in

Figure

5-1SOPEXAMPLE

5-1(P153)X=?液位指示器Low-lever:

1ABBCACX=AB+BC+ACTruth

tableA

BCABBCACX00000000010000010000001101011000000101001111010011111111steps：logiccircuitRelation

of

inputsand

outputsCombinational

logic

analysis由給定的邏輯圖逐級寫出邏輯關系表達式。用邏輯代數(shù)或卡諾圖對邏輯代數(shù)進行化簡。列出輸入輸出狀態(tài)表并得出結論。AND-OR

Invert

LogicEXAMPLE 5-1-2X=AB+BC+AC

=

ABBCAC=

(

A

+

B)(B

+

C)(

A

+

C)Truth

tableA

BCABBCACX00000010010001010000001101001000001101001011010001111110Exclusive-OR

LogicABX000011101110Two

equivalent

ways

of

implementing

the

exclusive-NOR.不同的電路可能實現(xiàn)同一個邏輯命題。Circuit

AfunctionCircuit

B…5-2 Implementing

Combinational

Logic組合邏輯電路的實現(xiàn)From

Boolean

expression

to

logiccircuitGiven

a

Boolean

expression,

create

alogic

circuit

that

implements

thatexpression.From

truth

table

to

logic

circuitGiven

a

truth

table,

create

a

logic

circuitthat

implements

that

table.From

Booleanexpression

to

logic

circuit-

Given

a

Booleanexpression,

create

a

logic

circuit

that

implementsthat

expression.Logic

circuit

for

X

=

AB

+

CDE.From

truth

table

to

logiccircuit-

Given

a

truth

table,

create

a

logic

circuit

that

implements

that

table.AINPUTBCOUTPUTXPRODUCT

EARM0000001001000111ABC1001ABC101011001110-Sum-of-productsformBoolean

SOPexpression

from

the

table

by

ORing

the

product

termsfor

which

X=1

isX

=

ABC

+

ABCA

taskthe

logiccircuitstepsCombinational

logic

design

(implement)a.

Taska

truth

table.a minimum

expression.b.

truth

tablec.

Expressiona

expressionthe logic

circuitAn

ApplicationLight

monitor

with

serious

faultsImplement

a

logic

circuit

for

A

traffic

light

monitor

systemnormal

operationABCY00010010010001111000101111011111Y

=

AB

C

+

ABC

+

ABC

+

ABC

+

ABCY

=

AB

C

+

ABC

+

ABC

+

ABC

+

ABCAB

CABC00

01111001100

11101ACABBCY

=

AB

C

+

AC

+

AB

+

BCY

=

AB

C

+

AC

+

AB

+

BCThe

logic

circuit

for

A

traffic

light

monitor

systemABCF00000010010001111000101111011111例：設計三人表決電路（A、B、C）。每人一個按鍵，如果同意則按下，不同意則不按。結果用指示燈表示，多數(shù)同意時指示燈亮，否則不亮。真值表首先指明邏輯符號取“0”、“1”的含義。三個按鍵A、B、C按下時為“1”，不按時為“0”。輸出是F，多數(shù)贊成時是“1”，否則是“0”。根據(jù)題意列出真值表。ABCF0000001001000111100010111101111100

01

11

10A010

0

1

00

1

1

1ABc.

畫出卡諾圖，并用卡諾圖化簡：真值表BCBCACF

=

AB

+

BC

+

CAd.

根據(jù)邏輯表達式畫出邏輯圖。F

=

AB

+

BC

+

CA若用與、或門實現(xiàn)=

AB

+

BC

+

CA=

AB

BC

CAF

=

AB

+

BC

+

CA若用與非門實現(xiàn)For

the

input

waveform

in

Figure

5-29

,

what

logic

circuit

willgenerate

the

output.（一）設計一個舉重裁判表決器。設舉重比賽有三個裁判，一個主裁判和兩個副裁判。杠鈴完全舉上的裁決由每一個裁判按一下自己面前的按鈕來確定。只有當兩個或兩個以上裁判（其中必須有主裁判）判明成功時，表示“成功”的燈才亮。（要求用與非門實現(xiàn)）（二）某設備有開關A、B、C，要求僅在開關A接通的條件下，開關B才能接通；開關C僅在開關B接通的條件下才能接通。違反這一規(guī)程，則發(fā)出報警信號。設計一個由與非門組成的能實現(xiàn)這一功能的報警控制電路。（要求用與非門實現(xiàn)）（三）設計一個路燈控制電路，要求實現(xiàn)的功能是：當總電源開關閉和時，安裝在三個不同地方的三個開關都能獨立地將燈打開或熄滅；當總電源開關斷開時，路燈不亮。（要求用異或門和與門實現(xiàn)）（四）設計一半加器電路.（要求用與非門實現(xiàn)）Applications5-3 The

Universal

Propertyof

NAND

and

NOR

GatesNAND

and

NOR

gates

are

“universal”

because

theycan

used

to

produce

any

of

the

other

logic

functions.The

NAND

Gate

as

a

Universal

Logic

ElementThe

NOR

Gate

as

a

Universal

Logic

ElementThe

NAND

Gate

as

a

Universal

Logic

ElementNAND

Gate

as

an

Inverter?Quote:

Inverters

can

also

be

considered

nand

gates:AAHIGH??Two

NAND

Gates

as

an

AND

Gate?AB

=

ABThree

NAND

Gates

as

an

ORGateA

+

B

=

A

+

B

=

ABFour

NAND

Gates

as

OR

GateA

+

B

=

AB

=

ABThe

NOR

Gate

as

a

Universal

Logic

ElementNOR

Gate

as

an

InverterTwo

NOR

Gates

as

an

OR

GateThree

NOR

Gates

as

an

AND

GateFour

NOR

Gates

as

an

AND

Gate5-4 COMBINATIONAL

LOGIC

USING

NANDAND

NOR

GATENAND

LOGICNOR

LOGICNAND

LOGICA

NAND

gate

can

function

as

either

a

NAND

or

a

negative-OR

.AB=A+BNANDnegative-ORNAND

logic

for

X

=

AB

+

CD.Development

of

the

AND-OR

equivalent.NOR

LOGICA

NOR

gate

function

as

either

a

NOR

or

a

negate-AND.A+B=ABNORnegative-ORNOR

logic

for

X

=

(A

+

B)(C

+

D)5-5 CIRCUIT

OPERATION

WITH

PULSE

WAVEFORMINPUTSDetermine

the

final

output

waveform

X

for

the

circuit

infigure

5-29

,with

input

waveforms

A,B

,and

C

as

shown.?Draw

the

timing

diagram

for

the

circuit

in

Figure

5-30shown

the

outputs

of

G1,G2.Figure

5–42Illustration

of

a

node

in

a

logic

circuit.Thomas

L.

FloydDigital

Fundamentals,

9eCopyright

?2006

by

Pearson

Education,

Inc