Chenyuanyuan@scu edu cn
Sponsored Links
This presentation is the property of its rightful owner.
1 / 94

第三章 组合逻辑原理 PowerPoint PPT Presentation


  • 107 Views
  • Uploaded on
  • Presentation posted in: General

计算机学院 陈媛媛 [email protected] 第三章 组合逻辑原理. 组合逻辑的定义. 逻辑电路中没有从输出到输入的反馈,且由功能完全的门系列构成,就称为 组合逻辑电路 。. ·. ·. Combinational Logic Functions. Inputs. ·. ·. Outputs. ·. ·. 真值表问题. 1. 开关方程与标准形式. 多变量卡诺图化简. 多输出函数. 2. 4. 6. Content. 卡诺图. 3. 混合逻辑组合电路. 5.

Download Presentation

第三章 组合逻辑原理

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


[email protected]


Combinational Logic Functions

Inputs

Outputs


1

2

4

6

Content

3

5



a,b1210

s10

m10

M10


    • y=2x

      x=y=


S3

m3

S2

m2

m4

S1

m1

  • 3-4123123


S3

m3

S2

m2

m4

S1

m1

s1,s2,s312310

m1,m2,m3,m4:10


  • 1ABCDA12

  • 1A,B,C,D

    10

    S10.


1

2

4

6

Content

3

5


  • 1 1 01


  • m7= abms

    m11=abms

    m15=abms

    M=abms+abms+abms

    M=bms+abms


  • m7= abms

    m11=abms

    m15=abms

    M=abms+abms+abms

    M=bms+abms

    bms, abms

    M=bms+abms

    m7m11m15

    M=m7+m11+m15

(1)(2)

(3)


  • 0 010


  • M0=a+b+m+s; M1=a+b+m+s;

    M2=a+b+m+s; M3=a+b+m+s;

    M4=a+b+m+s; M5=a+b+m+s;

    M6=a+b+m+s;M8=a+b+m+s;

    M9=a+b+m+s; M10=a+b+m+s;

    M12=a+b+m+sM13=a+b+m+s;

    M14=a+b+m+s;

    M=M0M1M2M3M4M5M6M8M9M10M12M13M14

    M=(a+b)(a+b+m)(a+b+m+s)(a+m)(a+m+s)


  • M0=a+b+m+s; M1=a+b+m+s;

    M2=a+b+m+s; M3=a+b+m+s;

    M4=a+b+m+s; M5=a+b+m+s;

    M6=a+b+m+s;M8=a+b+m+s;

    M9=a+b+m+s; M10=a+b+m+s;

    M12=a+b+m+sM13=a+b+m+s;

    M14=a+b+m+s;

    M=M0M1M2M3M4M5M6M8M9M10M12M13M14

    M=(a+b)(a+b+m)(a+b+m+s)(a+m)(a+m+s)

    a+b, a+b+m

    (a+b)(a+b+m)(a+b+m+s)(a+m)(a+m+s)

    M0M1

    M=M0M1M2M3M4M5M6M8M9M10M12M13M14

(1)(2)(3)


  • 1

    • M=abms+abms+abms=m7+m11+m15

      =m(7,11,15)

  • 0

    • M=(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)(a+b+m+s)

      (a+b+m+s)(a+b+m+s)

      =M0M1M2M3M4M5M6M8M9M10M12M13M14

      =M(0,1,2,3,4,5,6,8,9,10,12,13,14)


  • S=m11+m13 + m14 + m15= abcd+abcd+abcd+abcd

  • S=M0M1M2M3M4M5M6M7M8M9M10M12


  • step1

    step2xy(z+z)

    step3xyz+xyz.

  • step1

    step2x+y+zz

    step3(x+y+z)(x+y+z).


    • 1)10abcd:1010

      2)(1010)2=(10)10

      3)mk(k)

    • 1)01x+y+z:011

      2)(011)2=(3)10

      3)Mk(k)


  • 1.P=f(a,b,c)=ab+ac+bc ()

    step1: ab:c; ac:b; bc:a

    step2: P=ab(c+c)+a(b+b)c+(a+a)bc

    step3: P=abc+abc+abc+abc+abc+abc

    step4: P=m5+m4+m6+m7+m3

    =m(3,4,5,6,7)


2.Y(a,b,c,d)=abcd+bcd+ad ()

step1: abcd:; bcd:a; ad:b,c

step2: Y=abcd+(a+a)bcd+a(b+b) (c+c)d

step3:

Y=abcd+abcd+abcd+abcd+abcd+abcd+abcd

step4: Y=m9+m15+m7+m3+m13

=m(3,7,9,13,15)


  • 3.T=f(a,b,c)=(a+b)(b+c) ()

    step1 a+b:cb+c: a

    step2: T=(a+b+cc)(aa+b+c)

    step3 T=(a+b+c)(a+b+c)(a+b+c)(a+b+c)

    step4 T=M2M3M6=M(2,3,6)


4.Y(a,b,c,d)=(a+b)(b+c+d) ()

step1: a+b: c,d b+c+d:a;

step2: T=(a+b+cc+dd)(aa+b+c+d)

step3:

T=(a+b+c+d)(a+b+c+d)(a+b+c+d)(a+b+c+d)(a+b+c+d)(a+b+c+d)

step4:T=M0+M1+M2+M3+M7+M15=M(0,1,2,3,7,15)


  • :

    P=f(w,x,y,z)=wx+yz

    T=f(a,b,c,d)=(a+b+c)(a+d)

  • Ans:

    P=f(w,x,y,z)=wxyz+wxyz+wxyz+wxyz+wxyz+wxyz+wxyz

    =m(2,4,5,6,7,10,14)

    T=f(a,b,c,d)= (a+b+c+d) (a+b+c+d) (a+b+c+d) (a+b+c+d) (a+b+c+d) (a+b+c+d)

    =M(4,5,8,10,12,14)


    • step1

    • step2step1

    • step3step2


  • f1(a,b,c)= abc + abc + abc + abc = m1 + m2 + m4 + m6

    = (1,2,4,6) = (0,3,5,7) = (a+b+c)(a+b+c)(a+b+c)(a+b+c)



1

2

4

6

Content

3

5



01

A

02B

13B

23A


AB

A

B

0

1

00

01

11

10

0

m0

m2

m0

m2

m6

m4

0

1

m1

m3

1

m1

m3

m7

m5

AB

CD

00

01

11

10

00

m0

m4

m12

m8

C

01

m1

m5

m13

m9

m3

11

m7

m15

m11

10

m2

m6

m14

m10


2

0

1

0

0

1

B

A

1

1

1

0

0

1

0

2

3

1





    • step1

    • step2

    • step3

    • step410


AB

10

00

01

11

C

0

1

  • 1.

  • 2.

  • 1

1

1

1

1

1


BC

10

00

01

11

A

0

1

  • 2

1

1

1

1

1


ab

10

00

01

11

c

0

1

  • f(a,b,c) = ac + abc + bc

    step1

    step2


ab

10

00

01

11

c

0

1

step3

f(a,b,c) = ac + abc + bc

=ac(b+b)+abc+(a+a)bc

=abc+abc+abc+abc+abc

=abc+abc+abc+abc

step4:

1

1

1

1


XY

XY

10

00

01

11

10

00

01

11

Z

Z

1

1

1

1

1

0

0

1

1

1

1

1

1

  • f1(x,y,z)= m(2,5,6,7)

  • f2(x, y, z)=m(0,1,2,3,6)


ab

10

00

01

11

c

0

1

1

1

1

1

1


1248


YZ

00

01

11

10

WX

m0

m1

m3

m2

00

m4

m5

m7

m6

01

m12

m13

m15

m14

11

m8

m9

m11

m10

10

2

4

8

161.


1

1

1

1

1

1

1

1

1

1

1

  • (A,B,C,D) = m(0,1,2,3,4,5,6,7,8,10,13).

    step1

    step2

A

BD

AB

00

01

11

10

CD

00

1

1

1

BCD

1

1

1

01

1

1

11

1

1

1

10

g(A,B,C,D) = A+BD+BCD


ab

10

00

01

11

c

1

1

1

0

1

1

  • :

    f(a,b,c) = ac + abc + bc

    =a(b+b)c+abc+(a+a)bc

    =abc+abc+abc+abc+abc

    =abc+abc+abc+abc

    = ac+ab+bc

abc

bac

cab


ab

10

00

01

11

c

0

1

  • :

ACB

1

1

1

1

1

BAC


xy

z

00

01

11

10

0

1

1

1

1

1

xy

z

1

1

1

1

1

  • f1(x,y,z)= m(2,5,6,7)

    f2(x, y, z)=m(0,1,2,3,6)

f1(x, y, z) = yz + xz

f2(x, y, z) = x+yz


1

1

1

1

1

1

1

1

1

1

1

  • (1) 1

  • (2) 12n1

  • (3) ()

  • (4)

  • (5)


  • :

  • (PI):

    ACDABCD,BCD

  • (EPI):

    ABCBD

AB

CD

00

01

11

10

1

00

1

01

1

1

11

1

1

10

1

BCD

ABC

ABCD

ACD

BD


b

ad

ab

00

01

11

10

cd

1

1

00

1

1

1

01

1

1

1

11

ab

1

1

1

10

acd

acd

  • ab,acd,acd,ad,b

  • abb.

  • acd ad.

  • b, ad, acd

  • b, ad, acd .


  • f2(a,b,c,d),

  • f2bd.

acd

bd

abd

abc

bcd

acd

abc

ab

10

00

01

11

cd

1

00

1

1

1

01

1

1

11

1

1

1

10


`

  • f(a,b,c,d) = m(0,1,4,5,8,11,12,13,15).

    5

    ac,cd,acd.

  • Ans:

    f(a,b,c,d) = cd + ac + bc + acd

bc

cd

ab

cd

1

1

1

1

ac

1

1

1

1

1

abd

acd


xy

z

00

01

11

10

1

1

1

0

1

1

1

1

F(x,y,z)=(0,2,3,4,5,7)

6

Ans:

F(x,y,z)=xz+yz+xy

F(x,y,z)=yz+xy+xz

xy

z

00

01

11

10

1

0

1

1

1

1

1

1


  • f(a,b,c,d) = (0,3,4,5,7,11,13,15)

  • Ans:

    f(a,b,c,d) =acd+cd+bc

ab

cd

1

1

1

1

1

1

1

1


F(w,x,y,z)=(0,1,4,5,9,11,13,15)

F(a,b,c,d)=(0,1,2,4,5,6,8,9,12,13,14)

F(a,b,c,d)=(1,3,4,5,7,8,9,11,15)

F(w,x,y,z)=(1,5,7,8,9,10,11,13,15)


F(w,x,y,z)=(0,1,4,5,9,11,13,15)

wx

10

00

01

11

yz

00

1

1

1

1

01

1

1

1

11

1

10

ANS:F(w,x,y,z)=wy+wz


ab

cd

10

10

00

00

01

01

11

11

ab

cd

00

00

01

01

11

11

10

10

F(a,b,c,d)=(0,1,2,4,5,6,8,9,12,13,14)

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

F(a,b,c,d)=c+ad+bd


ab

10

00

01

11

cd

00

01

11

10

F(a,b,c,d)=(1,3,4,5,7,8,9,11,15)

1

1

1

1

1

1

1

1

1

ANS:F(a,b,c,d)=cd+ad+abc+abc


wx

10

00

01

11

yz

00

01

11

10

F(w,x,y,z)=(1,5,7,8,9,10,11,13,15)

1

1

1

1

1

1

1

1

1

F(w,x,y,z)=yz+xz+wx


  • ()


  • d()10


  • (dont care minterms)

    • (d)


b1b0

00

01

11

10

b3b2

00

0

0

0

0

01

0

1

1

1

11

d

d

d

d

10

1

1

d

d

8421BCD


A=f(w,x,y,z)=(5,6,7,8,9)+

d(10,11,12,13,14,15)

B=f(w,x,y,z)=(1,2,3,4,9)+

d(10,11,12,13,14,15)

C=f(w,x,y,z)=(0,3,4,7,8)+

d(10,11,12,13,14,15)

D=f(w,x,y,z)=(0,2,4,6,8)+

d(10,11,12,13,14,15)


A=w+xz+xy

B=xy+xz+xyz

C=yz+yz

D=z


cd

ab

01

11

00

10

0

1

0

1

00

1

1

0

1

01

0

0

d

d

11

10

1

1

d

d

0

1

0

1

1

1

0

1

0

0

d

d

1

1

d

d

0

1

0

1

1

1

0

1

0

0

d

d

1

1

d

d

f = acd+ab+cd+abc

f = acd+ab+cd+abd


    • 0

    • 01



a+b+c+d

cd

ab

00

01

11

10

00

1

1

1

1

1

1

1

0

01

  • F = (a+b)(a+c)(a+b+c+d)

0

0

1

1

11

0

0

0

0

10

a+c

a+b


AB

10

00

01

11

CD

00

01

0

0

0

0

11

0

10

0

C+D

F=(C+D)(A+B+D)(A+B+C)

A+B+C

A+B+D


1

2

4

6

Content

3

5




  • (Quine-Mcluskey)


1

2

4

6

Content

3

5


  • LEDLEDLED


1

1

F=AB

F=A+B

L:

H:


  • step1:

    step2:

    step3:


=

+

=

L

A

B

AB

L

=

AB

&

A

A

1

B

B


=

=

+

L

A

B

A

B

L

=

A

+

B

A

&

A

1

B

B




  • step1:

    step2

    step3


3

1

2


H

H

H

H=D+C(A+B)


1

2

4

6

Content

3

5



AB

AB

00

00

01

01

11

11

10

10

1

1

0

0

1

1

1

1

1

1

C

C

  • . F1=f(a,b,c)=(2,6,7)

    F2=f(a,b,c)=(1,3,7)

F1=ac+bc

F1=ac+abc

F2=bc+abc

F2=bc+ab


F1=ac+bc

F1=ac+abc

F2=bc+abc

F2=bc+ab


  • Login