[Math] Sum of Product and Product of sum for (AB+C)(B+C’D)’

Question

I am having a little trouble trying to converting the expression into sum-of-products and product-of-sums form. Not sure if i am doing the expression correctly. But this was what i was able to do.

I started out using Demorgan law:

(AB+C)(B+C'D)'

what i did was:

(AB+C)(B+C'D)'

(AB+C) (B'(C+D'))

(AB+C) (B'C+B'D')

ABB'C +ABB'D'+CB'C+CB'D'

B'C+CB'D'

Are my steps correct?

Answer 1

Your work is correct thus far: You can go further:

$\begin{align} B'C+CB'D'& = B'C(1)+B'CD'\\ &=B'C(1+D')\\ & = B'C(1) \\ &= B'C \end{align}$

This is now in both SOP and POS form.