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)=AB'+A'B+AB
(2) Y2(A,B,C)=AB'+B+(A+C')'
(3) Y3(A,B,C,D)=A+B'CD+A'BD
(4) Y4(M,N,P,Q)=MN'Q'+P'Q'+M'N'PQ'
【正确答案】(1) Y1(A,B,C)=AB'+A'B+AB
=(AB'+AB)+(A'B+AB)
=A(B'+B)+B(A'+A)
=A+B
(2) Y2(A,B,C)=AB'+B+(A+C')'
=A+B+A'C
=A+B+C
(3) Y3(A,B,C,D)=A+B'CD+A'BD
=A+B'CD+BD
=A+(B'C+B)D
=A+(C+B)D
=A+BD+CD
(4) Y4(M,N,P,Q)=MN'Q'+P'Q'+M'N'PQ'
=MN'Q'(P+P')+(M'N'+M'N
+MN'+MN)P'Q'+M'N'PQ'
=(MN'P'Q'+MN'PQ'+M'N'PQ'+M'N'P'Q')+P'Q'
=(MP'+MP+M'P+M'P')N'Q'+P'Q'
=N'Q'+P'Q'
【答案解析】