How to convert between Sum Of Products and Product of sums?

Question

I have a Boolean expression. we'll call it F.

for instance, F = ab' + ad + c'd + d'.

Assuming I did all the necessary steps too get F complement , i.e. F'.

I got: F' = b'd + ac'd'.

How do I get the Product of sums form of F?

Answer 1

$$F=(F')'=(b'd+ac'd\,')'=(b'd)'(ac'd\,')'=(b+d\,')(a'+c+d)\;.$$

(Note: I did not check your $F'$.)

Because of the way the De Morgan laws work, the complement of a product of sums is always a sum of products, and the complement of a sum of products is always a product of sums.