Question

Multiply out to get SOP of 3 terms each of 3 variables. (B + C’ + D’) (A’ + B + C) (A’ + C’ + D) (A’ + C) (C + D)

Answer 1

Solution for the question is provided below, please comment if any doubts:

The given POS relation is:

(B + C’ + D’) (A’ + B + C) (A’ + C’ + D) (A’ + C) (C + D)

Now multiply in,

= (A’B+A’C’+A’D’+B+BC’+BD’+CB+CD’) (A’ + C’ + D)(A’C+C+A’D+CD)

=

(A’B+A’C’+A’D’+A’B+A’BC’+A’BD’+A’CB+A’CD’+A’BC’+A’C’+A’C’D’+C’B+BC’+C’BD’+ A’BD+A’C’D+BD+BC’D+CDB) (A’C+C+A’D+CD)

=

A’BC+A’D’C+A’BC+A’BCD’+A’CB+A’CD’+ A’BCD+A’CBD+A’CDB +

+A’BC+A’CD’+A’BC+A’BCD’+A’CB+A’CD’+ A’BD+BD+CDB +

+A’BD+A’C’D+A’BD+A’BC’D+A’CDB+A’BC’D+A’C’D+C’BD+BC’D+A’BD+A’C’D+A’BD+A’BC’D+A’CDB

+ A’BCD+A’BCD+A’CBD+ A’BCD+BCD+CDB

Now reduce the terms,

=

A’BC+A’CD’+ A’BCD’+ A’BCD+BD+A’C’D

=A’BC+A’CD’+A’BCD’+A’C’D

=A’BC+A’CD+A’C’D

Thus the SOP term with 3 terms with 3 variables is: A’BC+A’CD+A’C’D