Question

数电:用公式化简法化简逻辑函数 F=AB+A非C+

数电:用公式化简法化简逻辑函数 F=AB+A非C+B非C
F=(A+B非)(B+C非)(C+D非)(D+A非)

Answer 1

F=AB+A'C+B'C=AB+(A'+B')C=AB+(AB)'C=AB+C

F=(A+B')(B+C')(C+D')(D+A')

=A(B+C')(C+D')(D+A')+B'(B+C')(C+D')(D+A')
=(AB+AC')(C+D')(D+A')+B'C'(C+D')(D+A')
=AB(C+D')(D+A')+B'C'(C+D')(D+A')
=ABC(D+A')+B'C'D'(D+A')
=ABCD+A'B'C'D
一级一级乘下来，总有AA'XX形式成为0项，所以越展开起简单

Answer 2

F=AB+A'C+B'C=AB+(A'+B')C=AB+(AB)'C=AB+C

F=(A+B')(B+C')(C+D')(D+A')

=A(B+C')(C+D')(D+A')+B'(B+C')(C+D')(D+A')
=(AB+AC')(C+D')(D+A')+B'C'(C+D')(D+A')
=AB(C+D')(D+A')+B'C'(C+D')(D+A')
=ABC(D+A')+B'C'D'(D+A')
=ABCD+A'B'C'D
一级一级乘下来，总有AA'XX形式成为0项，所以越展开起简单