boolean algebra problem

u24c02 said:

Thanks, and
I'm trying to convert*SOP (Sum of Products) to POS (Product of Sums).

The question is like this.

ABC +AB'C'+AB'C+ABC'+A'B'C

I just want to know some technic how to convert SOP to POS? I got thus like this but I can't find any more.

ABC +AB'C'+AB'C+ABC'+A'B'C =A(BC+B'C'+B'C+BC')+A'B'C
=A(1+1)+A'B'C

Would you please help me ? How to convert this?

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harpv said:

@u24c02

For your first question :

There could also be something like this :

Code:

ab' + c
= ab' + c + ca + cb'  // from  a + ab = a
= ab' + c(a + b' + 1)

So basically the answer you are looking for isn't unique.

For the second question :

Apply DeMorgan's law :

Code:

F = ABC +AB'C'+AB'C+ABC'+A'B'C 

F' = A'B'C' + A'BC' + A'BC (the SOP of minterms not present in F)

F = (F')' = (A'B'C' + A'BC' + A'BC)'

I believe the rest you can work out yourself.

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