How to convert this expression to the standard POS form?

Question

A'B + CD + BD' + AB'C

I know that the standard POS form must contain all variables in each sum term. But I don't know how to start to convert this expression to the standard form. Please advise.

Answer 1

Generalize from these examples:

$AB + CD= (A+C)(A +D)(B+C)(B+D)$

$AB+CD+EF=(A+C+E)(A+C+F)(A+D+E)(A+D+F)(B+C+E)(B+C+F)(B+D+E)(B+D+F)$

$AB+CDE=(A+C)(A+D)(A+E)(B+C)(B+D)(B+E)$

See how this works? You need to find all the ways of picking one literal from each term.

So, in your case you get $2 \cdot 2 \cdot 2 \cdot 3=24$ terms .... but many can be removed. For example, your first term would be $A'+C+B+A$, which equals $1$, and can thus be removed from the POS.

Another thing you can do is to first rewrite your expressin as $B(A'+D')+C(D+AB')$, which you can then work out to $(B +C)(B +D +AB')(A'+D'+C)(A'+D'+D+AB')$. The last term can be removed thanks to the $D'+D$, and the second term simplifies to $B +D +A$, giving as a final result $(B+C)(B+D+A)(A'+D'+C)$