问答题
将下列逻辑函数式化为与非—与非形式。
(1) Y1(A,B,C)=A'BC'+B'C+AC
(2) Y2(A,B,C)=(A'B'+B'C'+ABC')'
(3) Y3(A,B,C,D)=∑m(0,2,4,6,8,10)
(4) Y4(A,B,C,D)=((AB)'C')'D+CD'
【正确答案】(1) Y1(A,B,C)=A'BC'+B'C+AC
=((A'BC'+B'C+AC)')'
=((A'BC')'(B'C)'(AC)')'
(2) Y2(A,B,C)=(A'B'+B'C'+ABC')'
=(A'B'C'+A'B'C+AB'C'+ABC')'
=(m0 +m1 +m4 +m6) '
由于m0+m1 +m4+m6=(m2+m3+m5+m7)',故得到
Y2(A,B,C)=((m2 +m3 +m5 +m7)')'
=(m'2m'3m'5m'7)'
=((A'BC')'(A'BC)'(AB'C)'(ABC)')'
(3) Y3(A,B,C,D)=∑m(o,2,4,6,8,10)
=A'D'+B'D'
=((A'D'+B'D')')'
=((A'D')'(B'D')')'
(4) Y4(A,B,C,D)=((AB)'C)'D+CD'
=(AB+C')D+CD'
=ABD+C'D+CD'. =((ABD+C'D+CD')')'
=((ABD)'(C'D)'(CD')')'
【答案解析】