问答题
将下列逻辑函数式化为与或非形式。
(1) Y1(A,B,C)=AB'+A'B
(2) Y2(A,B,C,D)=A'B'D'+AB'D'+BD
(3) Y3(A,B,C,D)=∑m(1,2,4,6,9,11,12,14)
(4) Y4(M,N,P,Q)=∑m(2,3,4,6,8,9,13,15)
【正确答案】(1) Y1(A,B,C)=AB'+A'B
=AB'C'+AB'C+A'BC'+A'BC
=m2 +m3 +m4 +m5
=(m0 +m1 +m6 +m7)'
=(A'B'C'+A'B'C+ABC'+ABC)'
=(A'B'+AB)'
(2) Y2(A,B,C,D)=A'B'D'+AB'D'+BD
=∑m(0,2,5,7,8,10,13,15)
=(∑m(1,3,4,6,9,11,12,14))'
=(B'D+BD')'
(3) Y3(A,B,C,D)=∑m(1,2,4,6,9,11,12,14)
=(∑m(0,3,5,7,8,10,13,15))'
=(A'CD+AB'D'+B'C'D'+BD)'
(4) Y4(M,N,P,Q)=∑m(2,3,4,6,8,9,13,15)
=(∑m(0,1,5,7,10,11,12,14))'
=(M'N'P'+M'NQ+MN'P+MNQ')'
【答案解析】