完整版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
2210 = 2*8
1
+ 6*8 0 = 268
268 = 2 6 = 1011Q
010110
101102 = 00010110= 1^6
2 1 0
10810 = 1*8 + 5*8 + 4*8 = 1548
1548 = 1 5 4 = 11011002
001101100
110110Q = 0110(100= 6C 16
6 C
1 0 - 1
13.12510 = 1*8 1 + 5*8 0 + 1*8 1 = 15.18
15.18= 1 5. 1 = 1101.0012
001 101 001
1101.001 = 1101.0010= D.216
D
2
131.62510 = 2*8 2 + 0*8 1 + 3*8 0 + 5*8 "1 =
203.58
203.58 = 2 0 3. 5= 10000011.101
010 000 011 101
10000011.10!= 10000011.1010= 83.A 16
8
3
A
1-1
数字电路答案 第一章习题
(1) 1-2 (1)
1011012= 101101= 558
1011012= 0010(10仁
2D
558= 5*8 1 + 5*8 0 = 4510
11100101= 011{0010仁
345
1110010!= {1100101= E^
6
E 5
3458 = 3*8 2 + 4*8 1 + 5*8 0 = 22910
(1)
168 = 1*8 1
+ 6*8 0
= 1410
168= 16= 11102
001110
11102= 1110= E 16
1728 二 1*8 2
+ 7*8 1
+ 2*8 0
1728 = 1 7 2 = 11110102
001111 010
11110102 01111010 7A 16
7 A
61.538 = 6*8 1 + 1*8 0 + 5*8 1 + 3*8 2 = 49.6721。

61.538 = 6 1.5 3 = 110001.101011
110 001 101 011
110001.101011 = 00110001.10101100= 31.AC 16
3
1
A C
2 10 1
126.748 = 1*8 + 2*8 + 6*8 + 7*8 " 126.748 = 1 2 6. 7 4 = 1010110.1111
001 010110 111100
1010110.1111= 01010110.1111= 56.F 16
5 6 F
1-4
1-3 101.0011= 101.001100= 5.148
101.001!= 0101.0011= 5.316
5.148 = 5*8 0 + 1*8"1+ 4*8 ■2 = 5.187510
100111.101 = 100{11.{01=
47.4
100111.101 = 00100111.{010= 27.A 16 47.58 4*81 7*80 5*8 1
39.625i 0
(1)
-2
+ 4*8 = 86.937510
2A
= 2 A = 101010,
16
00101010
1010102 = 101010= 528
I 5 I 2
1 0
528= 5*8 + 2*8 = 4210
(1)
(2)B2F16 = B 2 F = 101100101111
1011 00101111
101100101111 = 101100{l01f1仁54578
5 4 5 7
54578 = 5*8 3 + 4*8 2 + 5*8 1 + 7*8 0 = 2863。

D3.E16= D 3 .E = 11010011.111
1101 0011 1110
11010011.111= 011010011.(11= 323.7
8
f 2 3 7
323.78 = 3*8 2 + 2*8 1 + 3*8 0 + 7*8 " 1 = 211.8751o
1C3.F916= { C 3.{" 9 = 111000011.11111001
00011100 0^11 11111^1
111000011.11111001= {11000011.111{110010= 703.762
8
7 0 3 7 6 2
2 1 0 - 1 - 2 - 3
7*8 2 + 0*8 1 + 3*8 0 + 7*8 1 + 6*8 2 + 2*8 3=
451.97261。

1-5
(1) A(B C) AB AC
左式=右式，得证。

(2) A BC (A B)(A C)
703.7628 =
(1)
(3) A B AB
左式=右式，得证。

(4) AB A B
左式=右式，得证。

A B 左式右式
0 0 1 1
0 1 0 0
1 0 0 0
1 1 0 0
A B 左式右式
0 0 1 1
0 1 1 1
1 0 1 1
1 1 0 0 (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。

A B 左式右式
0 0 0 0
0 1 1 1
1 0 1 1
1 1 0 0
A B 左式右式
0 0 0 0
0 1 1 1
1 0 1 1
1 1 0 0
(2)
A+ BA+ 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+ CA= 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
(8) AB BC CA AB BC CA
1-6 (1) 左式=右式，得证。

A+ AB+ B = 1
证：A+ AB+ B = A+ B+ B = A+ 1= 1
证：A BA CD A ACD
A ACD A(1 CD) A
(8) A
证:
1-7 (1)
(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
BBC
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
原式=
C D AB BC CD DA
F i = ABC + ABC
F l A B C (A B C)
F
2
= A(B+ C)+ C(B+ D)
A BC (C BD)
F3= (A+ B)(C+ D)
F3 AB CD
F4 = F4
F5 = F5
F6 = (AB+ CD)(B+ AD)
ABC D BAD
AB+ ACB + D ABAC BD
A+ BC + B+ CD
F 6 A B C BC D
(7) F 7 = AC+ BDC + A+ BD
F 7 A C B D CAB D
(8)
F 8 = (A+ D)(B+ C)+ (A+ C+ B)AB+ CD
F 8 A D BC A CB A B C D
1-8
F i = (A+ B)(C+ D) F 2= (A+ B)(C+ D) F 2' = AB+ C D
F 3= A(B+ D)+ B(A+ C) F 3'= (A+ BD)(B+ AC) F 4 = (A+ BCD)(ABC+ D) F 4= A(B + C+ D) + (A+ B+ C)D F 5 = A+ B + C + D F 5= ABCD
F 6'= (B+ C)(C+ D)+ B+ (A+ D)C F 7 = BC + ADAC + C+ AB F 7= (B+ C)(A+ D)+ A+ CCA+ B
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)
(1)
F , = AB + CD (6)
F 6 = BC + CDB (AD+ C)
1-9 (1) F 1 = ABC + ABC + ABC + ABC
00 01 11 10
(2) F 2 = A+ BC+ CD A B C FD A
B C FD 0 0 0 (P 1
0 0 10 0 0 0 01 1 0 0 11
0 0 1
00 1 0 1 10 0 0 1 11 1 0 1 11
0 1 0 00 1 1 0 10 0 1 0 01 1 1 0 11 0
1 1 10 1 1 1 10 0
1
1
11 1
1
1
11
CD 00 01 11 10
1
1
(3) F 3 = AB+ B(C+ AD)
A B C DF A B C DF 0 0 0 00 1 0 0 00 0 0 0 10 1 0 0 11 0 0 1
01 1 0 1 01 0 0 1 11 1 0 1 11 0 1 0 01
1 1 0
00 0 1 0 1
1
1 1 0 10 0 1 1 01 1 1 1 00 0
1
1
11
1 1
1
10
CD 。

01 11 10 (4) F 4 = (A+ B+ C)(A+ B+ C)(A+ B+ C)
(5) F 5= (BD+ C)(C+ AD)
A B C D A B C D
0 0 0 0 1 0 0
0 0 0
1 0 0 1
0 0 1
1 0 1 0
0 0 1 1 1 0 1 1
0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0
0 1 1
1 1 1 0 0 1 1 1 1 1 1 100
01
1
1
10
00 01 11 10
0 0 1 1
0 0 1 1
0 0 1 1
0 1 1 1
(6) F6 =(AB+C D)(BC+DA)(AC+BD)
A B C D A B C D
0 0 0 0 1 0 0
0 0 0
1 0 0 0
0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0
CD 00 01 11 10
00
11
10
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
(7) F7= A+ BC+ BA + C + D
A B C FD )A B C FD
0 0 0
1
1 0 0 10
0 0 0
1
1
1 0 0 11
0 0 1
1 0 1 10
0 0 1
1
1 0 1 11
ABpD 00
01 11 10
0 1 0
( 1 1 0 10
00 1 1 0 0
0 1 0
1 1 1 0 11
01 0 0 1 0
0 1 1
( 1 1 1 10
11
1 1 1 1
0 1 1 1 1 1 1 1
11
10 1 1 1 1 (8) F g ABD BC C A D DAC BD
1-10
标准与或式:
F ABCD ABCD ABCD ABCD ABCD ABCD ABCD
标准或与式:
1111
1]01
1100
1][1 co
01
1
10
00 01 11 10
1-11
1-12 1-13 (1)F i
⑵F2
⑶F3
⑷F4
⑹F6
⑺F7
(8)
F8
(1)F1
⑵F2
⑶F3
⑷F4
⑹F6
⑺F7
(8) F8
(b) F
CDABCDAB
CDABCDAB
0,2,4,567
0,2,3,4,5,12,1
3,15
O,1,2,4
,5
2,4,5,6,7,14
,15
O,3,4,5
,6
0,1,3,4,5 ,
8,10,11,12 ,13,14,15
O,2,5,
6
1,4,5,7,11
,14
0,7
2,3,5,6,7,13
,15
6,7,11,14,
15
0,1,2,3,4,6,7,10,
12,14
3,4,5,
7
0 ,1,5,
8,9 ,10,11,13
2,3,5
,7
0,2,4,7,9,12
,15
1,3,6,10,11
,12
0,2,4,5,7,8,9,13,1
4,15
0,3,4,6,8,9,1
3,15
AB+ BCD = A+ B+ BCD = A + AB+ BC + A+ C = A+ B+ C + B = A+ B+ AB(C+ D)= AB+ AB(C + D) = A+ B AB+ AC + B C + A? B =AB+ AC + BC + AB+ AB =A B+ AB+ (AC+ AB) + BC =A+ A+ BC = 1 BD+ ABCD + A+ B+ C
AB+ (A+ C)(D+ A+ B)+ (C+ D)E =AB + AD + CD +=C + AB(CD + CD )+
AB (CD + CD )
=C + CD + CD = C + D
AB+ BC + CA+ AB= AB + BC + C A+ A+ B= A+ C+ B+ C = 1
1-15 (1)
AB+ BC+ AC
(2)
ABC+ BC+ AD+ CD
1-14
1,2,5,7,10,11,1
2,14
(1) A + =BD + ABCD + ABC =BD + =BD + AC(D+ B) AC
ABC + CDE =AB + AD + CD + BC+ E
C + ABC
D + CD + (A+ B)(CD + CD ) (8) ABCOO 01 11 10
ABC+ ABCD+ ABCD+ AC = AB+ AC + BCD + BCD
(4)
B(C+ AD)+ AC(B+ D)
B + AC+ BD
(5)
B(C? D) ACD + BCD + BCD
0 /1
J
0 u
00 01 11 10
CD 00
01 J1
10
ABC+ BC+ AD+ CD= BC + AC+ D
(3) ABC+ ABCD + ABCD + AC
AB 00 c
0 0
y
W 0 0
01 11
10
11 10
0 0
1
1
0 0
01
1
10
00
AB 'CD )00 01 11 10 00 0 八 0
01 0
1
11 0
0 u 10
V
B(C ? D) ACD + BCD + BCD = CD + BCD
(6)
ABC+ BCD+ AD+ A(B+ CD)
ABC+ BCD + AD+ A(B+ CD)= ABD + ABD+ AC
(7)
ABC + CD + AC + BD + ACD
CD
ABC + CD + AC + BD + ACD = AC + BC + BC + D
(8)
ACD+ ABCD+ AB(C+ D)+ D
0 0
0 0 c 0
7
0 fc
丿
V
p
V
00
01
110
AB "CD 00 01
11
10 00
01 1
10
(3) F 3(A,B,C,D)=
? m(0,2,4,6,8,10,13,15)
ACD+ ABCD+ A B (C+ D) + D= A+ B+ C+ D
1-16
(1)
F i (A,B,C,D)= ? m(0,1,3,4,5,9,10,14,15)
F 1(A,B,C,D) = AC+ ABD+ BCD + ABC+ ACD
(2)
F 2(A, B,C,D)= ? m(2,3,6,8,913,15)
F 2
(A, B,C,D) = ABC+ ACD + ABD+ ABC
J 7
0 0 c
A
w
AB^ 00 01 11 10
0 0 c
0 0 0
y 0 c n
0 c
A
00 01 100 01 11 10
01 1
(6) F 6(A, B,C,D)=
? M
(3,4,7,8,11,12,15)
F 3(A, B,C,D)= BD + AD + ABD (4)
F 4(A,B,C,D)= ? m(0,l23,5,7,9,10,13)
F 4(A ,B ,C ,D )= AB+ C D + B DC + AD
(5)
F 5(A,B,C,D)= ? M (1,3,7,8,9,10,14)
0 0
c
r
AB^ 00 01 11 10
00
丿 0
0 N 0
V
0 厂
V
丿
U
00、
01 1
/
01 11 10
、
01 110
00
01
110
CD 00 01 11 10
F5(A, B,C,D)= AD + BC+ ACD
? M (6) F6(A, B,C,D)=
(3,4,7,8,11,12,15)
(1) F 1(A,B,C)=
? m(0,2,3,7)
(7) F 7(A,B,C,D)= ? M
(2,5,6,10,12,13,14) F 7(A ,B ,C ,D )= CD + BC + AC D (8) F 8(A,B,C,D)= ? M (1,2,3,6,7,13,14,15)
F 8(A , B ,C ,D )= CD + AB+ ABC
1-17
AB 'C
‘00
01 11 10
00 c
代
01 0 『
0 N 11 0 1 0 N 10
V
w
F 6(A, B,C,D) =
CD + CD
+ ABC
A 0
0 0
0 0 0
0 0
V
A
00 01 11 10
CD 00 01 11 10 AB^CD 00 01” 11 10 00
7
0 w 0 1
0 0 0 1丿
0 £
A
V
01 110
F 1(A ,B ,C )= (B + C)(A+ C )
(2)
F 2(A,B,C,D)= ? m(0,1,7,8,10,12,13)
F 2(AB ,C ,D )= (A + B + C )(A + B + C)(B + C+ D )(A+ C+D )(A + B + D )
(3)
F 3(A,B,C,D)= ? m(1,2,3,7,8,9,12,14)
F 3(A, B,C,D)= (A+ C+ D)(A+ B+ D)(B+ C+ D)(A+ C+ D)(A+ B+ C)
(4)
F 4(A,B,C,D)= ? m(0,2,5,7,8,10,13,15)
1 1 €
c ◎
1
1 1
u 1 €
1
00 01 11
10 C D
00 01 11 10
1 1 1
1 € 1
u
1
1
1
3
00
01 11 10
CD 00 01 11 10
F 4(A,B,C,D)= (B+ D)(B+ D)
(5)
F 5(A,B,C,D)= ? M (1,2,5,6,7,10,13,14)
F 5(A, B,C,D)= (C+ D)(A+ C+ D)(B + C + D)(A+ B+ D)
(6)
F 6(A, B,C,D)= ? M (0,4,6,9,10,11,12,15)
1
1
A
1
3 0 1
w 1 n 1
1
1
V
00 01 11
10 CD 00 01 11 10
AB^CDOO 00
1
V
1
1 1 厂
丿 1 1
1
£
9
1
10
01
11 10
F
6
(A, B,C,D)= (A+ C+ D)(B+ C + D)(A+ B+ D)(A+ B+ D)(A+ B+ C)(A+ C+ D)
(7)F7(A, B,C,D)= ? M (2,3,4,10,11,13,14,15)
AB^OO 01 11 10
1 1 1
1 1
w
1 1
1 c
01 1
F 7(A,B,C,D) = (A+ B+ C+ D)(B+ C)(A+ C)(A+ B+ D)
(8)
F 8(A,B,C,D)= ? M(0,3,5,6,8,10,12,15)
C D
00… 01 11 10
00 \0/ 1
1
01 1
© 1
® 11
1 © 1 10
1
1
€
F 8(A, B,C,D)= (B+ C+ D)(A+ C + D)(A+ B+ D)(A+ B+ C+ D)
=(A+ B+ C+ D)(A+ B+ C+ D)(A+ B+ C+ D)
1-18
(1)F 1 = ABCD + ABCD + ABCD
F 1 = BD
00 1 1
3
1
1
1
1 €
1 1
攻
01 11
10 00 01 11 10
约束条件 AB+ AC= 0
0 0
X X X X
7
X
/
O0S 1
CDQ 。

01
11 10
、
CD B \
00
01 11 10
05 3 0 0
01 0
11
X
丿 X
1L
X X
7
F 2 = BD + BD
(3)
F 3 = BCD + BCD + ABCD
F 3 = BD + AD+ BD
(4)
F 4 = ABCD + BCD + ABCD
F 4 BC AD
(5)
F 5= AC+ BD+ ABC+ ABCD (2)F 2= A BD + A BD + BCD
约束条件 AB+ AC = 0
约束条件BC+ CD = 0
K
厂
丿 0 X
£
:X 0
约束条件BD+ BD = 0
X
f
X
丿 0
J 丿 X
X
X
约束条件ABCD + ABCD = 0
00 01
11 10 00 01 11 10
11 10
F 5= D + BC+ AC
1-19 F 1(A,B,C,D)=邋 m(0,1,3,5,10,15)+ d(2,4,9,11,14)
F 1(A,B,C,D) = AB+ AC+ AC
(2) F 2(A,B,C,D)=
邋m(0,1,5,7,8,11,14)+ d(3,9,15)
AB^CDOQ 01 11
10
00
11
10
V /
丿
0 [
0 0
V
£
A
01
f
1」
V
0 0
X
J
11 10
CD 00 01 11 10
(6) F 6= AB+ BC+ CD 约束条件
? d(0,1,2,6) = 0
00 X X
A
X
厂
丄
丿
V
F 6 = (1)
11 10 B+ CD
01 11 10
F 2(A,B,C,D) = BC+ AD+ CD+ ABC
(3)
F 3(A,B,C,D)=邋m(2,6,9,10,13) +
F 3(A, B,C,D)= AD + CD + AB
(4) F 4(A, B,C,D)=邋m(1,3,7,11,13) +
(5)
F 5(A,B,C,D)=邋m(2,4,6,7,12,15)
+
0 厂
0 0
X
X [1
X
X 0
K
丿
X
00 01 11
10 F 4(A,B,C,D)= D
CD 。

01 11 10
d(0,1,4,5,8,11)
A
X| 0
k
0 1 1
0 0
w 寸 ———,
d(5,9,10,12,14,15)
d(0,1,3,8,9,11)
00
01
11 10
C D
00 01 11 10
F 5(A, B,C,D)= CD + CD+ AD (6)
F 6(A,B,C,D)=邋m(2,3,6,10,11,14)+ d(0,1,4,9,12,13)
F 6(A ,B ,C ,D )= CD + BC
(7)
F 7(A, B,C,D)=邋m(3,5,6,7,10)+ d(0,1,2,4,8,15)
F 7(A,B,C,D)= A+ BD
(8) F 8(A,B,C,D)=
邋m(0,4,8,11,12,15)+
d(2,3,6,7,13)
AB'^DOO 01
11 10
00 11 10
X
A
卩
0 1
k F
0 1
X V
01 X X V
X
h
X X
0 h
X
£
00 01 11
10 CD
00 01 11 10
—
1 1
0 X
7 0
11 CD
AB
0 01 11 10
7
F8(A,B,C,D)= CD+CD
第二章习题2-1
a) Z i= AB+ BC = B(A+ C)
真值表：
b) Z2= A+ BC + D = ABCD
真值表:
A B C D F A B C D F
0 0 0 0
1 0 0 0 0
1
0 0 0 1 0 1 0 0 1 0
0 0 1 0 0 1 0 1 0 0
0 0 1 1 0 1 0 1 1
0 1 0 0 0 1 1 0 0 0
0 1 0 1 0 1 1 0 1
0 1 1 0 0 1 1 1 0
0 1 1 1 0 1 1 1 1
C)Z3= C+ D+ B+ A? E C+ D+ B+ Ae E= (C + D)gB+ Ae E 真值表:
A B C D E F
0 0 0 0 0 0
0 0 0 0 1 1
0 0 0 1 0 1
0 0 0 1 1 0
0 0 1 0 0 1
0 0 1 0 1 0
0 0 1 1 0 1
0 0 1 1 1 0
2-2 a)表达式：Z = B+ CACA? B C? A ABC
真值表:
b）表达式：X7排C A_
Y 二AB + BC + AC 真值表:
2-3
表达式：Z= ADBBCDADC = BCD 真值表:
A B C D Z A B C D Z
0 0 0 0
1
1 0 0 0 1
0 0 0 1 1 1 0 0 1
1
0 0 1 0 0 1 0 1 0 0
0 0 1 1 1 1 0 1 1
1
0 1 0 0 1 1 1 0 0 1
0 1 0 1 1 1 1 0 1
1
0 1 1 0 1 1 1 1 0
1
0 1 1 1 1 1 1 1 1
1 波形图:
A
B
C
D
Z
2-4
1)
2)
A —
B —
3)
F
4)
&
5)
F
6)
F6=(B+ CD -+ E = EB + (A+ B)C D E
F
2-5
1) F = ABCD
F
2)F = ABC AD
F 3)F = ACDBCD
F
F
5)F = ABBCCA
F 6)F = ABBCC A
F
1) F = A+ B+ C + D
A 一 1 a
B 1
F
D
2) F=A+D+B+C
3) F = A+ C + B+ D+ C + A+ C+ A+ D
4)F=A+B+A+B+C+D+C+D
m3 5— 1
F
A 1
■> 1
1 >
11 1
F
F
5)F = A+B+B+C+C+A
6)F =
2-7 F 0 1 0 1
1 0 1 0
0 1 0 1
1 0 1 0
(1)卡诺图及表达式:
1
00 01 11
10 AB"CD 00 01 A+ B+ C + A+ D
F
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)(A+ B+ C+ D)
(2 )电路图:
2-8
(1 )真值表:
(2)卡诺图及表达式:
AB 工 0 0 0 0 £
0 © 0 0 0
0 0 © 0 £
y 0
0 0 0
c
7 0
00 01 11 10 S2S1S0000 001 011 010 110 111 101 100
F = Si S 0 AB + S 2S o B + ASS + BS 2 S 0 + ABSS 0 + ABSS o + AS 2S + ABS 1S 0 (3 )电路图:
F
2-9 (1 )真值表:
A B C D F A B C D F 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 )卡诺图及表达式:
F = BC + BD + A BD = B CB D AB D
(3 )电路图:
B
Ct & & >
A t &h_^
& >
& >
D 2-10 (1)真值表:
7 0 £
0 c n 0
0 0 0 0
:A 0
AB 00
01 11 10 X
得Z = ABBC AC (3 )电路图:
(1)
①真值表:
A i A o
B i B 0 F A i A o B i B 0 F 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 F = A i A 0B i B 0A i A 0B i B 0A i A 0B i B 0A i A 0B i B 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
A 00 01 10
00 01 11 10
(2)
① 真值表:
②卡诺图及表达式:
F
A o
B i B o
A i
F = A 1A 0B 1B 0A 1A 0B 1B 0A 1A 0B 1B 0A 1A 0B 1B 0
③电路图:
(3)
①真值表:
00 01 11
10 B 1 B o
② 卡诺图及表达式:
F = A 0B 0
③电路图:
(4)
① 真值表:
00 01 11 10 B 1B 0
A 1A \ F
A
B o
A i A o B1 B0 F A1 A0 B1 B0 F
0 0 0 0 1 1 0 0 0 1
0 0 0 1
1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0
F = A0B0
③电路图:
(5)
①真值表:
A o &
B o F
A 1 A Q
B 1 B Q F A 1 A Q B 1 B Q F 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0
② 卡诺图及表达式:
F = A Q B Q + A Q B Q = A Q B Q A Q B Q
③ 电路图:
2-12
(1 )真值表:
S 1 S 2 Z
Q Q Q
Q 1 1
1 Q 1
1 1 Q
B 1 B Q
A 1A K 00 QQ 10
01 11 Q
V 7 Q
Q Q 厂
丿 Q Q
k
Q A A Q
10 F。