北科大853电路理论与自动控制原理电子数电课件

Basic

Combinational

Logic

Circuits

AnalysisImplementing（

Design

）

Combinational

Logic组合逻辑电路的实现(设计）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组合逻辑电路分析和设计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（与-或逻辑电路）AND-OR-Invert

Logic（与-或-非逻辑电路）Exclusive-OR

Logic（异-或逻辑电路）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由给定的逻辑图逐级写出逻辑关系表达式。用逻辑代数或卡诺图对逻辑代数进行化简。列出输入输出状态表并得出结论。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.不同的电路可能实现同一个逻辑命题。Circuit

AfunctionCircuit

B…5-2 Implementing

Combinational

Logic组合逻辑电路的实现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：设计三人表决电路（A、B、C）。每人一个按键，如果同意则按下，不同意则不按。结果用指示灯表示，多数同意时指示灯亮，否则不亮。真值表首先指明逻辑符号取“0”、“1”的含义。三个按键A、B、C按下时为“1”，不按时为“0”。输出是F，多数赞成时是“1”，否则是“0”。根据题意列出真值表。ABCF0000001001000111100010111101111100

01

11

10A010

0

1

00

1

1

1ABc.

画出卡诺图，并用卡诺图化简：真值表BCBCACF

=

AB

+

BC

+

CAd.

根据逻辑表达式画出逻辑图。F

=

AB

+

BC

+

CA若用与、或门实现=

AB

+

BC

+

CA=

AB

BC

CAF

=

AB

+

BC

+

CA若用与非门实现For

the

input

waveform

in

Figure

5-29

,

what

logic

circuit

willgenerate

the

output.（一）设计一个举重裁判表决器。设举重比赛有三个裁判，一个主裁判和两个副裁判。杠铃完全举上的裁决由每一个裁判按一下自己面前的按钮来确定。只有当两个或两个以上裁判（其中必须有主裁判）判明成功时，表示“成功”的灯才亮。（要求用与非门实现）（二）某设备有开关A、B、C，要求仅在开关A接通的条件下，开关B才能接通；开关C仅在开关B接通的条件下才能接通。违反这一规程，则发出报警信号。设计一个由与非门组成的能实现这一功能的报警控制电路。（要求用与非门实现）（三）设计一个路灯控制电路，要求实现的功能是：当总电源开关闭和时，安装在三个不同地方的三个开关都能独立地将灯打开或熄灭；当总电源开关断开时，路灯不亮。（要求用异或门和与门实现）（四）设计一半加器电路.（要求用与非门实现）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