# Boolean Algebra - Simplest POS / SOP

1. Oct 12, 2011

### xenocid3r

Hey all

So i just need some clarification, though I hope I am posting in right section (this is not a HW Q)

I was told to find the simplest Product of Sums(POS) and Sum of Products(SOP)

1st 2nd 3rd
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now i know that POS mean that (A+B+C')(A+B'+C)(C+D). Is the simplest form of this expression is that I need to have ABCD in every term there. or is this form is already simplest. Do I need to add D to the first 2 terms and A and B to the 3rd?
I mean do i need to use the distributive law in order to minimize an expression like that?

I was trying to look in my text book but could understand it very clearly. Would appreciate if someone can explain that to me.

P.S. the expression above is not part of the homework, I just gave something random. I am trying to understand the concept and not to solve it.

Thanks for anyone who will try to help me here

Xeno

Last edited: Oct 12, 2011
2. Oct 12, 2011

### MisterX

No, if you had A, B, C, and D in every product term, then the expression would be a product of maxterms. The expression you posted is simpler than the equivalent product of maxterms.

3. Oct 12, 2011

### xenocid3r

another thing. in a sum of products, can I have ABC+BD+A'BCD'. Is this consider a minimal SOP? I know I can combine the above terms to get rid of few literals. but just for the sake of it, lets assume it isn't possible.