Minimize the following expression in a Sum of Products and b

Minimize the following expression in (a) Sum of Products and (b) Product of Sums forms:

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

Solution

It is already in the POS form.

(A’ + B’ + D)(A’ + D’) (A + B + D’)(A + B’ + C + D)
= (A\' + A\'D\' + A\'B\' + A\'D) (A + AB\' + AC + AD + AB + BC + BD + AD\' + B\'D\' + CD\')
= A\'(1 + D\' + B\' + D) (A(1 + B\' + C + D + B + D\') + BC + BD + B\'D\' + CD\')
= A\' (A + BC + BD + B\'D\' + CD\')
= A\'BC + A\'BD + A\'B\'D\' + A\'CD\'

(which is the reqd. SOP form)