数字电路与逻辑设计课后习题测验答案蔡良伟第三版.docx
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数字电路与逻辑设计课后习题测验答案蔡良伟第三版
数字电路答案
第一章习题
1-1
(1)2210=2*81+6*80=268
268=26=1011Q
010110
101102=00010110=1%
16
210
(2)10810=1*8+5*8+4*8=1548
1548=154=110110Q
001101100
110110C2=01101100=6C16
6C
10-1
(3)13.12510=1*81+5*80+1*81=15.18
15.18=15.1=1101.0012
001101001
1101.00!
=1101.0010=D26
D2
2101
(4)131.62510=2*8+0*8+3*8+5*8-=203.58
203.58=203.5=10000011.101
010000011101
10000011.10!
=10000011.1010=83.A16
83A
1-2
(1)
1011012=
101101=558
55
1011012=
00101101=2D16
2D
558=5*8
'+5*80=4510
(2)
11100101
=011100101=3458
345
1110010!
=11100101=E516
E5
3458=3*82+4*81+5*80=229®
(3)101.0011=101.001100=5.148
514
101.001!
=0101.0011=5.36
53
5.1^4=5*H81*+8-4=*85o1875
(4)100111.101=100111.101=47.4
474
100111.101=00100111.1010=27A16
27A
101
47.5^4*87*805*8-39.62510
1-3
(1)168=1*81+6*80=1410
168=16=11102
001110
1110=11=低16
E
210
(2)1728=1*82+7*81+2*8°=12210
1728=172=11110102
001111010
11110102二01111010二7A16
7A
10-1-2
(3)61.538=6*8+1*8+5*8+3*8=49.6721。
61.538=61.53=110001.101011
110001101011
110001.101011=00110001.10101100=31.AC16
31AC
21012
(4)126.748=1*8+2*8+6*8+7*8-+4*8-=86.937510
126.74=126.74=1010110.1111
001010110111100
1010110.1111=01010110.1111=56.F16
56F
1-4
(1)2人6=2A=1010102
00101010
1010102=101010=528
52
(2)B2F16=B2F=101100101111
101100101111
101100101111=101100101111=54578
5457
54578=5*83+4*82+5*81+7*80=286310
(3)D3.E16=D3.E=11010011.111
110100111110
11010011.111=011010011.111=323.78
3237
2101
323.78=3*8+2*8+3*8+7*8-=211.87510
(4)1C3.F916=1C3.F9=111000011.11111001
00011100001111111001
111000011.11111001=111000011.111110010=703.7628
703762
210.1.2・3
703.7628=7*8+0*8+3*8+7*8+6*8+2*8=451.97261。
1-5
(1)A(BC)二ABAC
A
B
C
左式
右式
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
左式=右式,得证。
(2)ABC-(AB)(AC)
A
B
C
r左式
右式
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
左式=右式,得证。
(3)AB=AB
A
B
左式
右式
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
左式=右式,得证。
(4)AB=AB
A
B
左式
右式
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
左式=右式,得证。
(5)ABCABC=1
A
B
C
r左式
右式
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
左式=右式,得证。
(6)abAb二abAB
A
B
左式
右式
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
左式=右式,得证。
(7)A二B=A二B
A
B
左式
右式
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
左式=右式,得证。
(8)AB亠BC亠CA=AB亠BC亠CA
A
B
C
「左式
右式
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
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:
ABACD二AACD二AaCD二A(1CD)=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?
BAB=A+B
证:
A?
BAB=AB+Ab+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=ABDABCDBCDADABCABCD(再加一次最后一项)
=BD(A+AC)+BCD+Ad+BC(A+AD)
=BD(A+C)+BCD+AD+BCAD
=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二BB二CC二D=ABBCCDDA
证:
原式=ABAbBCBCCDCD
=ABBCCDABBCCDADDA
=ABBCCDDAAbBCCDAD
=ABBCCDDAABBCCDDA
=ABBCCDDA
1-7
(1)Fi=ABC+ABC
=ABC(ABC)
(2)F2=A(B+C)+C(B+D)
爲h【ABC(CBD)
(3)F3=(A+B)(C+D)
=ABCD
(4)F4=(AB+CD)(B+AD)
F4二ABCDBAD
(5)F5=AB+ACB+DF5=ABACBD
(6)F6=A+BC+B+CD
尸6二ABcbCD
(7)F7=AC+BDC+A+BD
F7=ACBDCABD
(8)F8=(A+D)(B+C)+(A+C+B)AB+CD
Fg=AdbCACBABCd
1-8
(1)R=AB+CDFi'=(A+B)(C+D)
(2)F2=(A+B)(C+D)F2'=AB+Cd(3)F3=A(B+D)+B(A+C)F3=(A+BD)(B+aC)(4)F4=(A+BCD)(ABC+D)F4'=A(B+C+D)+(A+B+C)D(5)F5=A+B+C+DF5=ABCD
(6)F6=BC+CDB(AD+C)
F6=(B+C)(C+D)+B+(A+D)C
(7)F7=BC+ADAC+C+AB
F7=(B+C)(A+D)+A+CCA+B
(8)F8=ABC+A+CD(BD+C)+(BC+A+D)B+A+BC
F8'=(A+B+C)A(C+D)+(B+D)C(B+C)AD+BA(B+C)
1-9
(i)已=aBc+Abc+ABC+abc
ABC
F
000
1
001
0
010
0
011
1
100
0
101
1
110
0
111
1
00
01
11
10
1
0
1
0
0
1
1
0
(2)F2=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
CD0000011110011110
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
(3)F3=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
、CD
0
0
01
0
01
ABC00
01
11
10
1
1
1
00
0
0
1
1
0
0
1
11
1
0
1
11
0
1
0
01
1
1
0
00
01
1
1
1
1
0
1
0
11
1
1
0
10
11
0
0
0
0
0
1
1
01
1
1
1
00
10
0
1
1
1
0
1
1
11
1
1
1
10
(4)F4=(A+B+C)(A+B+C)(A+B+C)BC00011110
1
1
1
0
0
0
1
1
(5)F5=(BD+C)(C+AD)
A
B
C
D
A
B
C
D
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
10
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
0
1
1
1
10
0
1
1
1
1
1
1
1
CD0001111000011110
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
(6)F6=(AB+CD)(BC+DA)(AC+BD)
A
B
C
D
A
B
C
D
0
0
0
0
1
0
0
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
CD00011110
00
01
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
F1
)A
B
C
FD
0
0
0
1(
1
0
0
10
0
0
0
11
1
0
0
11
0
0
1
0(
1
0
1
10
0
0
1
01
1
0
1
11
0
1
0
0(
1
1
0
10
0
1
0
01
1
1
0
11
0
1
1
0(
1
1
1
10
0
1
1
11
1
1
1
11
(8)F8二AbDBCCADDACBD
ABCD
F
ABCD
F
dC00
1
1000
1
0001
1
ID01
1
0010
1
L010
1
0011
1
1011
1
0100
1
L100
1
0101
1
1101
1
0110
1
1110
0
0111
0
1111
0
1-10
标准与或式:
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
11
10
00
01
11
10
01
CD00
00
co
1
1
1
1
1
0
1
1
1
0
0
1
]
1
1
01
11
10
01
11
10
F=ABCDABCDABCDABCDABCDABCDABCD
标准或与式:
F=ABCDABCDABCDABCdABCDABCDABCDABCDABCD
1-11
(1)Fi八0,2,4,567
(2)F2八0,2,3,4,5,12,13,15
(3)F3二'、0,1,2,4,5
(4)F4八2,4,5,6,7,14,15
(5)F5八0,3,4,5,6
(6)F6=—10,1,3,4,5,8,10,11,12,13,14,15
(7)F7八0,2,5,6
(8)F8「1,4,5,7,11,14
1-12
(1)F^il:
':
.0,7
(2)F^il-2,3,5,6,7,13,15
(3)F3F'6,7,11,14,15
(4)F^il-0,1,2,3,4,6,7,10,12,14
(5)F^il'3,4,5,7
(6)F6八0,1,5,8,9,10,11,13
(7)F7-IU:
23,5,7
(8)F8Fl」10,2,4,7,9,12,15
1-13
⑻F=「1,3,6,10,11,12
FTU10,2,4,5,7,8,9,13,14,15
(b)F八0,3,4,6,8,9,13,15
F訓|;1,2,5,7,10,11,12,14
1-14
(1)A+AB+BCD=A+B+BCD=A+B
(2)AB+BC+A+C=A+B+C+B=1(3)A+B+AB(C+D)=AB+AB(C+D)=A+BAB+AC+BC+A?
B=AB+AC+BC+AB+AB⑷=AB+AB+(AC+AB)+BC=A+A+BC=1BD+ABCD+A+B+C=BD+ABCD+ABC=BD+AC(D+B)=BD+AC
AB+(A+C)(D+A+B)+(C+D)E
(6)=AB+AD+CD+ABC+CDE
=AB+AD+CD+BC+E
C+ABCD+CD+(A+B)(CD+CD)
(7)=C+AB(CD+CD)+AB(CD+CD)
=C+CD+CD=C+D
(8)AB+BC+CA+AB=AB+BC+CA+A+B=A+C+B+C=1
1-15
(1)AB+BC+AC
AB+BC+AC=A+BC
(2)ABC+BC+AD+CD
11
10
0
Z|
X
y
0
11
0
0
u
K
0
V
X
00
01
11
10
01
CD00
ABC+BC+AD+CD=BC+AC+D(3)Abc+abCd+ABCD+AC
h
0
0
R
0
0
w
0
0
0
0
00
01
11
10
011110
0
0
0
0
J
匚
cl
Lx
0
0
ABC+ABCD+ABCD+AC=AB+AC+BCD+BCD(4)B(C+AD)+AC(B+D)
CD
AB、00011110
00
01
11
10
B(C+AD)+AC(B+D)=AB+AC+BD
(5)B(C?
D)ACD+BCD+BCD
AB
00
0
八
0
0
0
11
0
h
0
0
y
0
V
0
0
00
01
11
10
01
11
10
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
00
11
10
V
y
0
k
J
0
p
0
k
01
11
01
CD00
10
ABC+CD+AC+BD+ACD=AC+BC+BC+D
(8)ACD+ABCD+AB(C+D)+D
01
11
10
卜
A
A
7
1J
A
0
w
寸
X
z
x
00
01
11
10
CD00
ACD+ABCD+AB(C+D)+D=A+B+C+D
1-16
(1)F1(A,B,C,D)=?
m(0,1,3,4,5,9,10,14,15)
厂
A
0
7
0
0
0
0
c
0
0
00
01
11
10
CD0001|1110
F1(A,B,C,D)=AC+ABD+BCD+ABC+ACD
(2)F2(A,B,C,D)=?
m(2,3,6,8,913,15)
0
0
c
0
0
0
V
0
c
0
0
0
00
01
11
10
CD00011110
F2(A,B,C,D)=ABC+ACD+ABD+ABC
(3)F3(A,B,C,D)=?
m(0,2,4,6,8,10,13,15)
00
01
0
0
p
0
0
0
c
0
0
0
11
CD00011110
1
F3(A,B,C,D)=BD+AD+ABD
(4)F4(A,B,C,D)=?
m(0,1,2,3,5,7,9,10,13)
C
0
J
0
0
1
1,
0
0
0
V
0
00
01
11
10
CD00