# Boolean Algebra Simplest Sum of Products

#### th3rapy

Joined Jan 25, 2012
4
This is the only one in homework that is giving me problems and I am stuck:
It wants simplest sum of products
A C' D' + B C' D + A B' C'

any suggestions?

#### Georacer

Joined Nov 25, 2009
5,182
Have you tried doing a Karnaugh Map? Post it here.

#### th3rapy

Joined Jan 25, 2012
4
we haven't covered that yet (few chapters away). The solution manual has A C' D' + B C' D + A B C' + A B' C' as the next step but i don't know how they get to that. I've read the chapter and have tried many things and can't seem to get it.

#### Georacer

Joined Nov 25, 2009
5,182
I think it would be a good idea if you posted a photo or screen capture of the question in your textbook. At least try to state it exactly as it is written. The second expression you wrote is equivalent to the first one, but points to the opposite direction of what the question asks.

#### th3rapy

Joined Jan 25, 2012
4
Question ask: Derive the simplest sum-of-products for the function f= A C' D' + B C' D + A B' C'

Solution manual:

Equation given:
A C' D' + B C' D + A B' C'
Second step (this is the part I don't understand how they get it):
A C' D' + B C' D + A B C' + A B' C'
Third step (I understand this part):
A C' D' + B C' D + A C'
B C' D + A C'

I understand everything but the second step. I know I'm just missing something and I can't seem to figure it out

#### Georacer

Joined Nov 25, 2009
5,182
I know it is non intuitive and I admit that I wouldn't use this method for simplification.

What the manual does is to use the minterm #12 from AC'D' and minterm #13 from BC'D to create a new group with them and introduce the ABC' term. It doesn't make any sense and it's not supposed to.

This is why a Karnaugh map is the dominant tool for expression simplification.

#### th3rapy

Joined Jan 25, 2012
4
I think I figured out what the book wanted me to do.

We have the "Consensus Property" which states: xy + yz + x'z = xy + x'z

So I let AC' =z D' = x' BC' = y D=x

The original problem as the right hand side of the consensus property would give yz BC'AC' = ABC' which explains the second step on the solution manual.

I looked ahead at the k-table and it makes way more sense than just being able to see something like this. Thanks for the help