# Boolean Algebra

## Homework Statement

Convert the following expression into sum of products and products of sums

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

## Homework Equations

Distributive Property

## The Attempt at a Solution

for product of sums it would be (AB+C)(B+C'D) since it is already in this form.

When calculating sum of products I get...
(AB+C)(B+C'D) = ABB+ABC'D+CB+CC'D = ABB+ABC'D+CB+0D = ABB+ABC'D+CB
= A*1+ABC'D+CB = A+ABC'D+CB (this is where I get confused)
=A(1+BC'D)+CB
(I know 1+X=1 but what about 1+BC'D? Can I reduce this further of would A(1+BC'D)+CB be in the correct form?)

vela
Staff Emeritus
Homework Helper

## Homework Statement

Convert the following expression into sum of products and products of sums

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

## Homework Equations

Distributive Property

## The Attempt at a Solution

for product of sums it would be (AB+C)(B+C'D) since it is already in this form.
That's not a product of sums. You can't have products like AB in the expression.
When calculating sum of products I get...
(AB+C)(B+C'D) = ABB+ABC'D+CB+CC'D = ABB+ABC'D+CB+0D = ABB+ABC'D+CB
= A*1+ABC'D+CB = A+ABC'D+CB (this is where I get confused)
=A(1+BC'D)+CB
(I know 1+X=1 but what about 1+BC'D? Can I reduce this further of would A(1+BC'D)+CB be in the correct form?)
ABB ≠ A. Evaluate both sides with A=1 and B=0, for instance.

sum of products
Oh yes I see!
(AB+C)(B+C'D) = ABB+ABC'D+CB+CC'D = ABB+ABC'D+CB+0D = ABB+ABC'D+CB
=AB+ABC'D+CB
Then this would be in the correct form!

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