Final answer:
The Boolean expression (AB+C)(B+CD) expands to AB + CB in sum of products form and remains (AB+C)(B+CD) in product of sums form, applying Boolean algebra laws including distributive, idempotent, and absorption.
Step-by-step explanation:
To convert the expression (AB+C)(B+CD) into sum of products (SOP) and product of sums (POS) forms, we use the distributive law of Boolean algebra:
- For sum of products, the expression expands to:
- (AB)(B) + (AB)(CD) + (C)(B) + (C)(CD)
- A(BB) + A(BCD) + CB + (C)(CD)
- Since BB is equal to B (idempotent law):
- AB + ABCD + CB + CCD
- We can eliminate redundant terms (absorption law):
- AB + CB (since ABCD is covered by AB and CCD is covered by CB)
- For product of sums, expand and apply the distributive law again:
- ((AB)+C)((B)+(CD))
- This leaves the expression as is because it is already in POS form.