2.32
(2) Y2 ABD ABD BD
m(0,2,5,7,8,10,13,15) (m(1,3,4,6,9,11,12,14))
(BD BD)
CD
00 01 11 10
AB
00
11
01 1
1
11 1
1
10
11
(3) Y3 m(1,2,4,6,9,11,12,14) (m(0,3,5,7,8,10,13,15))
Y2 ABD AC BCD
(3) Y3 m(1,2,6,9,10,15) d(0,4,8,12)
Y3 AD BC BD ABCD
(4) Y4 ABCD ABCD ACD AB AC 0 将约束条件化为约束项之和形式得到: m10 m11 m12 m13 m14 m15 0
真值表
A B C D Y2 00000 00010 00101 00110 01001 01010 01100 01111 10001 10010 10100 10111 11000 11011 11101 11110
2.12 答案： (1) Z1(A, B,C) AB BC AC
((A B C) (A B C) (A B C) (A B C))
Y3 m(2,3,4,5,10,11,12,13) (m(0,1,6,7,8,9,14,15))
CD 00 01 11 10
AB
00 1 1
(BC BC)
01
((B C) (B C))
11
11 11
10 1 1
A B AC ABC
(3) Y3 A BCD ABD
A BCD BD A (BC B)D A (C B)D A CD BD
(4) Y4 MNQ PQ M NPQ
MNQ (P M NP)Q MNQ (P M N)Q MNQ PQ M NQ NQ PQ
Y1(A, B,C) m(0,3,4,7)
ABC ABC ABC ABC
(2)
Y2(A, B,C, D) m(2,4,7,8,11,13,14)
ABCD ABCD ABCD ABCD ABCD ABCD ABCD
(M N P) Q M NP(Q Q) Q(M M )(N N)(P P)
m(0,1,2,4,6,8,10,12,14)
2.9 答案：
(1)
真值表
A B C Y1 000 1 001 0 010 0 011 1 100 1 101 0 110 0 111 1
Y m(1,4,5,7)
真值表
ABC Y 000 0 001 1 010 0 011 0 100 1 101 1 110 0 111 1
ABC ABC ABC ABC
2.25 答案：
(1) Y1 AB AB AB
AB B A B
(2) Y2 AB B (A C)
(4) Y4 PQS PQRS PQR PRS
Y4 QS PQR RS
2.30
(1) Y1 m(1,2,4,7) d(3,5)
Y1 AB C AB
(2) Y2 m(1,2,3,8,9,10) d(12,13,14,15)
AD BD
(AD BD)
((AD)(BD))
(4) Y4 (( AB)C)D CD
(AB C)D CD ABD CD CD (ABD CD CD) ((ABD)(CD)(CD))
Y4 AD BD CD
2.31
(1)
Y1 ABC BC AC (ABC BC AC)
CD
00 01 11 10
AB
00 1
1
((ABC)(BC)(AC))
01 1
1
(2) Y2 (AB BC ABC)
2.27
(1) Y1 m(0,1,2,6)
Y1 AB BC
(2) Y2 AB AC BC CD
Y2 AB C D
(3) Y3 m(1,2,6,7,9,13,14)
Y3 ACD ABC BCD ACD BCD
AB(C C) BC(A A) AC(B B)
m(0,1,2,4)
真值表
A B C Z1 000 1 001 1 010 1 011 0 100 1 101 0 110 0 111 0
2.13 答案：
(1)
Y1(A, B,C) AB BC AC
第2章 逻辑代数基础
2.7 答案：
(1) Y (A, B,C) AB AC B
AB(C C) AC(B B) B(A A)(B B) ABC ABC ABC ABC ABC ABC
(4) Y (M , N, P,Q) ((M N P)Q)
(ACD BCD ABD BD)
CD
00 01 11 10
AB
00 1
1
01 1 1
11
1
10 1
1 1
2.33
Y1 ABC ABC ABC ABC m1 m2 m4 m7 (m0 m3 m5 m6 )
(ABC ABC ABC ABC)
(2) Y2 (A, B,C, D) (( A C) (B D))(B D)
2.15 答案： (b)
Y2 (A, B,C) (( ABC)(AB)(BC))
(d)
Y4 (A, B,C, D) (( A B)C (C D)B)
2.21 答案：
(ABC ABC ABC ABC) 11
(m0 m1 m4 m6 )
10 1
1
(m2 m3 m5 m7 )
(m2 )(ABC))
(3) Y3 m(0,2,4,6,8,10)