数字逻辑第一章习题(上)答案
第一章习题
1-1
(1)2210=2*81+6*80=268
268=2 6 =101102
010110
101102=00010110 =1616
1
6
(2) 10810=1*82+5*81+4*80=1548 1548=1 5 4
=11011002 001101100
11011002=01101100 =6C 16
6
C
(3)13.125-110=1*81+5*80+1*8=15.18 15.18=1 5. 1
=1101.0012 001101001
1101.0012=1101.0010 =D .216
D
2
(4)131.625110=2*82+0*8+3*80+5*8-1=203.58 203.58=2 0000 3. 011 5101
=10000011.1012
010 10000011.1012=10000011.1010 3
=83. A 1 6
8
A
1-2
(1)1011012=101101 =558
5
5
1011012=00101101 2
=2D 16
D
558=5*81+5*80=4510 (2)111001012=011100101 =3458
3
4
5
111001012=11100101 =E 516
E
5
3458=3*82+4*81+5*80=22910
(3)101.00112=101.001100 =5.148
5
1
4
101.00112=0101.0011 =5.316
5
3
5. 184=
50*+8
-11
*+8
-
42
=*8
5. 1 0
1875(4)100111.1012=100111.101 4
7
=47.48
4
100111.1012=00100111.1010 =27. A 16
2
7
A
47. 58=4*81+7*80+5*8-1=39. 62510
1-3
(1)168=1*81+6*80=1410 168=1001110
6 =11102
11120= 11=10E 1 6
E
(2)172218=1*8+7*8+2*80=12210 1728=1 7 2
=11110102 001111010
11110102=0111 1010 =7A 16
7
A
(3)61.5328=6*81+1*80+5*8-1+3*8-=49.67210
61.538=6 1. 5 3 =110001.1010112
[1**********]1
110001.1010112=00110001.10101100 =31. AC 16
3
1
A
C
(4)126.7428=1*8+2*81+6*80+7*8-1+4*8-2=86.937510 126.748=1 2010 6. 110 7=1010110.11112 111 4
001100
1010110.11112=01010110.1111 5
=56. F 16
6
F
1-4
(1)2A 16=2A =1010102 0010 1010
1010102=101010 =528
5
2
5210
8=5*8+2*8=4210
(2)B 2F 16= B 2F =[***********]010 1111
[1**********]12=[1**********]1 =54578
5
4
5
7
54578=5*83+4*82+5*81+7*80=286310 (3)D 3. E 16=1101 D 3 . E
=11010011.1112 00111110
11010011.1112=011010011.111 =323.78
3
2
3
7
323.78=3*82+2*81+3*80+7*8-1=211.87510 (4)1C 3. F 916=10001 C 1100 30011 . F 1111 91001
=111000011.111110012
111000011.111110012=111000011.111110010 =703.7628
7
3
7
6
2
703.76228=7*8+0*81+3*80+7*8-1+6*8-2+2*8-3=451.9726101-5
(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。
(3)A +B =
左式=右式,得证。 (4)AB =+
左式=右式,得证。 (5)A +BC +BC =1
左式=右式,得证。 (6)A +B =AB +
左式=右式,得证。 (7)A ⊕B =A ⊕
左式=右式,得证。
(8)A +B +C =B +C +A
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 +B +CD =A +CD =A +A CD =A (1+CD ) =A (3)AB +A C +BC =AB +C
证:AB +A C +BC =AB +(A +B ) C =AB +ABC =AB +C
(4)AB +A +C +B (D +E ) C =AB +A C
证:AB +A +C +B (D +E ) C =AB +A C +BC (D +E ) =AB +A C
(5)A ? B AB =A +B
证:A ? B AB =AB +AB +AB =A +AB =A +B
(6)AB +BC +CA =ABC +ABC
证:AB +BC +C A =(A +B )(B +C )(C +A ) =ABC +ABC (7)ABD +BCD +AD +ABC +ABCD =AB +AD +BC
证:原式=A +C +D +D +A C +C (再加一次最后一项) =BD (A +A C ) +BCD +AD +BC (A +AD )
=BD (A +C ) +BCD +AD +BC AD
=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 =A +B +C +D 证:原式=A +B +B +C +C +
=A +C +D +B +B +C +A +
=A +B +C +D +B +C ++A
=A +B +C +D +A +B +C +D =A +B +C +
1-7
(1)F 1=ABC +ABC
1=(+B +)
(A ++C )
(2)F 2=A (B +C ) +C (B +D ) 2=(+B )
(C +)
(3)F 3=(A +B )(C +D )
3=A +
(4)F 4=(AB +CD )(B +AD )
4=(A +)(+D )+(+D )
(5)F 5=AB +A CB +D
5=(+B )(A ++)
(6)F 6=A +BC +B +CD
6=+C B +
(7)F 7=AC +BDC +A +BD
7=+C ++C +
(8)F 8=(A +D )(B +C ) +(A +C +B ) AB +CD
8=D +B +++
1-8
(1)F 1=AB +CD
F ' 1=(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 +C DB (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 )
1-9
(1)F 1=ABC +ABC +ABC +ABC
A B C F 0 0 0 10 0 100 1 000 1 111 0 001 0 111 1 001 1 1
1
(2)F 2=A +BC +CD
A B C DF A B C DF 0 0 0 001 0 0 010 0 0 101 0 0 110 0 1 001 0 1 010 0 1 111 0 1 110 1 0 001 1 0 010 1 0 101 1 0 110 1 1 011 1 1 010 1 1 1
1
1 1 1 1
1
(3)F 3=AB +B (C +AD )
A [1**********]101
1
1
[***********]1111111110
1
1
1
1
A B C D0 0 0 00 0 0 1F 00A B C D1 0 0 01 0 0 1F [1**********] 0 1 011 0 1 010 0 1 111 0 1 110 1 0 011 1 0 000 1 0 111 1 0 100 1 1 011 1 1 000 1 1 1
1
1 1 1 1
4)F 4=(A +B +C )(A +B +C )(A +B +C ) A B C F 0 0 0 10 0 110 1 000 1 111 0 001 0 101 1 011 1 1
1
5)F 5=(BD +C )(C +AD )
[***********]10
1
1
1
A [1**********]101
1
1
(
(
A B C DF A B C DF 0 0 0 001 0 0 000 0 0 101 0 0 110 0 1 011 0 1 010 0 1 111 0 1 110 1 0 001 1 0 000 1 0 101 1 0 100 1 1 011 1 1 010 1 1 1
1
1 1 1 1
1
6)F 6=(AB +CD )(BC +DA )(A C +BD ) A B C DF A B C DF 0 0 0 001 0 0 000 0 0 101 0 0 100 0 1 001 0 1 000 0 1 101 0 1 100 1 0 001 1 0 000 1 0 101 1 0 100 1 1 001 1 1 000 1 1 1
1 1 1 1
7)F 7=A +BC +B A +C +D
[***********]1111001110
1
1
1
[***********]0011000010
(
(
A B C DF A B C DF 0 0 0 011 0 0 010 0 0 111 0 0 110 0 1 001 0 1 010 0 1 101 0 1 [1**********] 1 0 001 1 0 010011000 1 0 101 1 0 110100100 1 1 001 1 1 011111110 1 1 111 1 1 11101111
8)F 8=B +
C +(A +D )+
A C +BD
11 (