Karnaugh Map from Boolean Expression

[nabelekt]

Hi,

I'm trying to figure out a few questions on a practice exam that I'm working on for my Intro to Logic Systems class and could use some help.

One of the questions (and the others are similar) says:

Determine the minimized realization in the sum-of-produicts form using literals of the function:
f(A,B,C) = $\Sigma$m(4,6) + $\Sigma$d(2,3,7)

The given answer is f(A,B,C) = AC'.

I know that $\Sigma$m(4,6) can be represented by AB'C' + ABC' and that $\Sigma$d(2,3,7) can be represented by A'BC' + A'BC + ABC, but beyond that I am not sure what to do. I think that I need to construct a Karnaugh map from the expression, but am not sure how to do it.

Any help is greatly appreciated. Thanks!

 

[NascentOxygen]

f(A,B,C) = $\Sigma$m(4,6) + $\Sigma$d(2,3,7)

Before embarking on a K-map, I suggest that you construct a truth table for your Boolean expression for f(A,B,C), and compare it with AC', to make sure you have that right.

 

[nabelekt]

Thanks for the reply. I'm pretty sure that I know how to construct a Karnaugh map given a truth-table. But I do not know how to construct a truth-table given an expression like that. Can you help me with that?

 

[NascentOxygen]

Don't you just OR those two expressions:
AB'C' + ABC' with A'BC' + A'BC + ABC?

I assume that is the way to go.