I was given this truth table on an exam the other day and was asked to find the simplest form using boolean algebra. To the right you see my unsimplified expression using the product of sums method and what I figured the answer would be.
I threw it in a K-map to see if my answer was right and it seems like I have an extra term. The K-map gives the simplest expression, and I can't for the life of me figure how to go from the expression to what I got from the K-map. To late to change my answer on the exam but how to get the answer is irking me. Iso help.

This post was edited by ROM on Dec 11 2014 08:40pm

The truth table states "Yes" for :
B and ( A or non C )

I would answer :

B.(A+Cbar)

which is the same as what you wrote : B.Cbar + A.B

What is the problem ?

using ' (prime) for bar:

BC' + ABC is what he got from simplifying the boolean expression.
BC' + AB is what he got from the kmap.

he's trying to understand how to go from the first line to the second using boolean algebra. it's clear they both work, but it's not obvious to me how to get rid of the second C using just boolean algebra.

My bad, I didn't read carefully enough.

BC' + ABC = B.(C' + AC)
whereas
BC' + AB = B.(C' + A)

So the problem is to show that C' + AC = C' + A

This is a well known rule for any boolean algebra.

You can write :

C' + AC = (C'+A).(C'+C), using the distributivity of + over .
and since C'+C = 1 :
C' + AC = (C'+A).1 = C'+A

Ahh thanks. So it was a combination of the distributive law and the + over . law.
I out the answer the Kmap gave me on the exam so I'm not worried I got it wrong. =P