问答题
用公式化简法将下列逻辑函数化为最简与或形式。
(1) Y1(A,B,C)=A'BC+AC'+B'C
(2) Y2(A,B,C)=A'B'+BC'+A(B+C)'
(3) Y3(A,B,C,D)=AB'CD+ABD+AC'D
(4) Y4(M,N,P,Q)=M'N'P'Q+M'P'Q'+MN'P'+M'PQ'
【正确答案】(1) Y1(A,B,C)=A'BC+AC'+B'C
=A'BC+AC'+B'C+A'B'C
=A'C+AC'+B'C
(2) Y2(A,B,C)=A'B'+BC'+A(B+C)'
=A'B'+BC'+AB'C'
=A'B'(C+C')+(A+A')BC'+AB'C'
=A'B'C+A'B'C'+ABC'+A'BC'+AB'C'
=(A'B'+AB+A'B+AB')C'+A'B'C
=1·C'+A'B'C
=A'B'+C'
(3) Y3(A,B,C.D)=AB'CD+ABD+AC'D
=AB'CD+AB(C+C')D+A(B+B')C'D
=AD(B'C+BC'+BC+B'C')
=AD
(4) Y4(M,N,P,Q)=M'N'P'Q+M'P'Q'+MN'P'+M'PQ'
=M'N'P'Q+M'(N+N')P'Q'+MN'P'(Q+Q')
+M'(N十N')PQ'
=M'Q'(N'P'+NP'+N'P+NP)
+N'P'(M'Q+M'Q'+MQ'+MQ)
=M'Q'+N'P'
【答案解析】