Question

数字电路化简 用公式法把这个题化成最简 或与 式

Answer 1

Y(ABCD)

=m0+m1+m2+m8+m9+m10+m15

=A'B'C'D'+A'B'C'D+A'B'CD'+AB'C'D'+AB'C'D+AB'CD'+ABCD

=A'B'C'+B'CD'+AB'C'+ABCD

=B'C'+B'CD'+ABCD

=B'(C'+CD')+ABCD

=B'(C'+D')+ABCD (吸收律)

=B'C'+B'D'+ABCD

=(B'C'+B'D'+ABCD)'' (关键变换,取再次非,后面用摩根律)

=((B'C')'·(B'D')'·(ABCD)')'

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

=((B+BC+CD+BD)(A'+B'+C'+D'))'

=((B+CD)(A'+B'+C'+D'))' (吸收律)

=(A'B+BC'+BD'+A'CD+B'CD)'

=(A'B+BC'+BD'+A'CD(B+B')+B'CD)' (添加(B+B'),使用吸收律)

=(A'B+BC'+BD'+B'CD)'

=(A'B)'·(BC')'·(BD')'·(B'CD)' (摩根律)

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

得证,关键在于吸收律与摩根律的使用,如果学过卡诺图的话,你会觉得使用卡诺图更加简单.