数字电路与逻辑设计课后习题答案蔡良伟(第三版)

数字电路答案

1

数字电路答案

第一章习题 1-1

(1) 2210 = 2*8 1 + 6*8 0 = 268

268 = 2 6 = 1011Q

010110

101102 = 00010110= 1^6

(2) 2 1 0

10810 = 1*8 + 5*8 + 4*8 = 1548

1548 = 15 4 = 110110Q

001101100

110110Q = 0110(100= 6C 16

6 C

(3) 1 0 - 1

13.12510 = 1*8 1 + 5*8 0 + 1*8 1 = 15.18

15.18 = 1 5? 1 = 1101.0012

001101 001

1101.00! = 1101.0010= D26

D 2

(4) 2 10 1

131.62510 = 2*8 + 0*8 + 3*8 + 5*8 - = 203.58

203.58 = 2 0 3. 5= 10000011.101

010 000 011 101

10000011.10!= 10000011.1010= 83.A 16

8 3 A

1-2

(1) 1011012 = 10100仁 558

5 5

1011012= 0010(101= 2D 16

2 D

1 0

558 = 5*8 + 5*8 = 4510

(2) 11100101 = 011{00{101= 3458

1110010! = {1100101= E%

E 5

3458 = 3*8 2 + 4*8 1 + 5*8 0 = 229?

数字电路答案

2 (3) 101.0011= 101.001100= 5.148

5 1 4

5.148 = 5*8 0 + 1*8 - I + 4*8 - 2 = 5.187510

(4) 100111.101 = 100{11.{01= 47.4

4 7 4

100111.101 = 0。100111.{010= 27.A 16

2 7 A

1 0 1 47.58 4*81 7*80 5*8 1 39.62510 1-3

(1) 168 = 1*8 1 + 6*8 0 = 1410

168= 16= 11102

001110

11102= |110= E 16

2 10

(2) 1728 = 1*8 2 + 7*8 1 + 2*8 ° = 12210

17 2 = 11110102

001111 Q 1Q

11110102 01111010 7A 16

7 A

1 0

- 1 - 2

(3) 61.538 = 6*8 + 1*8 + 5*8 + 3*8 = 49.6721° 61.538 = 6 1*5 3 = 110001.101011

0 001 101 Q

110001.101011 = 0011Q001.10101100= 31.AC 16

3 1 A C

2 1

Q 1 2

(4) 126.748 = 1*8 + 2*8 + 6*8 + 7*8 - + 4*8 - = 86.93751。

126.748 = 1 2 6? 7 4 = 1010110.1111 Q01 Q1Q11Q 11110Q 1010110.1111= 0101Q110.1111= 56.F 16

5 6 F 1-4

(1) 2A 6= 2 A = 10101Q 2

Q01Q 101Q

10101Q 2 = |01Q10= 528

5 2

(2) B2F 16 = B 2 F = 101100101111

1011 00101111

I Q

528= 5*8 + 2*8 = 421Q

101.001! = 仁 5.36

1728 =

数字电路答案

3

101100101111 = |011100{101{111= 54578

5 4 5 7

54578 = 5*8 3 + 4*8 2 + 5*8 1 + 7*8 0 = 286310

(3) D 3.E 16= D 3 .E = 11010011.111

1101 0011 1110

11010011.111= 01101。011.{1仁 323.78

3 2 3 7

2 10 1

323.78 = 3*8 + 2*8 + 3*8 + 7*8 - = 211.87510

(4) 1C3.F916= 1 C 3 . F 9 = 111000011.11111001

00b11100 0011 11111001

111000011.11111001= 1110OO011.111f10p1O= 703.7628 2 1 0 - 1

- 2 - 3 703.7628= 7*8 + 0*8 + 3*8 + 7*8 + 6*8 + 2*8 = 451.97261。

1-5

(1) A(B C) AB AC

左式=右式，得证。

(2) A BC (A B)(A C)

左式=右式，得证。

数字电路答案

(3) A B AB

左式=右式，得证。

(4) A B A B

左式=右式，得证。

(5) A BC ABC 1

左式=右式，得证。

(6) AB AB AB AB

左式=右式，得证。

(7) A B A B

左式=右式，得证。

4

数字电路答案

(8) AB BC CA AB BC CA

左式=右式，得证。

1-6

(1)A+ AB+ B = 1

证：A+ AB+ B = A+ B + B = A+ 1= 1

(2)A+ BA+ CD = A

证：A BA CD A ACD A ACD A(1 CD) A

(3)AB+ AC+ BC= AB+ C

证：AB+ AC+ BC = AB+ (A+ B)C = AB + ABC = AB+ C

(4)AB+ A+ C+ B(D+ E)C = AB+ AC

证：AB+ A+ C+ B(D+ E)C= AB+ 7C + BC(D+ E) = AB + AC

(5)A? B AB= A+ B

证：A? B AB= AB+ A B+ AB= A+ AB= A+ B

(6)AB + BC + C A = ABC + ABC

证：AB+ BC + CA = (A+ B)(B + C)(C + A) = ABC + ABC

(7)ABD + BCD+ AD+ ABC+ ABCD = AB+ AD+ BC

证：原式= ABD ABCD BCD AD ABC ABCD （再加一次最后一项）

=BD (A+ AC) + BCD + AD + BC(A+ AD)

=BD(A+ C)+ BCD + AD+ BCAD

5

数字电路答案

6

=BD(A+ C) + B(C + CD )+ AD =ABD + B(CD + C+ D)+ AD =B(AD + D)+ CB+ AD =(AB+ BD+ AD) + CB

=AB + AD + BC

(8) A

B B

C C D

AB

BC

CD DA

证：

原式=AB A B BC

BC CD CD

=AB BC

CD AB BC CD AD DA

=AB BC

CD

DA

AB BC CD AD

=AB BC CD DA

AB

BC CD

DA

=AB BC CD

DA

1-7

(1)

F i =ABC+ ABC

F 1

A B C (A B C)

(2)

F 2 = A(B+ C)+ C(B+ D)

爲 A BC (C BD)

(3)

F 3 = (A+ B)(C+ D)

F 3 AB CD

(4)

F 4 = (AB+ CD)(B+ AD)

F 4 A B C D BA D

(5)

F 5 = AB+ ACB + D F5 A B A C BD

(6) F 6 = A+ BC + B + CD

数字电路答案

7

F 6 AB C BC D

(7) F 7 = AC+ BDC + A+ BD (8) F 8 = (A+ D)(B+ C)+ (A+ C+ B)AB+ CD

F 8 AD BCACB A B C D 1-8

(1) F , = AB + CD

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

(2) F 2 = (A+ B)(C+ D)

F 2' = AB+ CD

(3) F 3= A(B+ D)+ B(A+ C)

F 3'= (A+ BD)(B+ AC)

(4) F 4 = (A+ BCD)(ABC+ D)

F 4= A(B + C+ D) + (A+ B+ C)D

(5) F 5 = A+ B+ C+ D

F 5'= ABCD

(6) F 6 = BC + CDB (AD+ C)

F 6'= (B+ C)(C+ D)+ B+ (A+ D)C

(7) F 7 = BC + ADAC + C+ AB

F 7= (B+ C)(A+ D)+ A+ CC A+ B

(8) F 8 = ABC + A+ CD (BD + C)+ (BC+ A+ D)B+ A+ BC

F 8'= (A+ B+ C)A(C+ D)+ (B+ D)C(B+ C)AD + BA(B+ C)

F 7