问答题
将下列逻辑函数化为最小项之和的形式。
(1) Y(A,B,C)=A'B+B'C
(2) Y(A,B,C)=((AB'C)'+C)'
(3) Y(P,Q,R,S)=P'R'S+P'QR+Q'R'S
(4) Y(A,B,C,D)=A'BCD+ABC'+B'D
【正确答案】(1) Y(A,B,C)=A'B+B'C
=A'B(C+C')+(A+A')B'C
=A'B'C+A'BC'+A'BC+AB'C
(2) Y(A,B,C)=((AB'C)'+C)'
=AB'CC'=0
(3) Y(P,Q,R,S)=P'R'S+P'QR+Q'R'S
=P'(Q十Q')R'S+P'QR(S+S')+(P+P')Q'R'S
=P'Q'R'S+P'QR'S+P'QRS'+P'QRS+PQ'R'S
(4) Y(A,B,C,D)=A'BCD+ABC'+B'D
=A'BCD+ABC'(D+D')+B'D(A+A')(C+C')
=A'BCD+ABC'D+ABC'D'+AB'CD+AB'C'D
+A'B'CD+A'B'C'D
【答案解析】