Simplifying Boolean Expressions: Minterms & Sum of Products

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Homework Statement

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

Express the function as sum of minterms, and find the ninimal sum of products.

Homework Equations

The Attempt at a Solution

How do I do this? I really don't know. I know it is easy though. Any help is appreciated!

 

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If I had some function:

f(a, b, c) = abc + abc'

then we can perform these logical manipulations:

f(a, b, c) = ab(c + c')

Now, c can either be a 1 or a 0. If c is 1, then c' is 0, and if c is 0, c' is 1. Therefore, the OR of c and c' is always 1, because only one of the arguments needs to be a 1 for OR to return 1. So we can now simplify and write:

f(a, b, c) = ab

So how does this all relate to your first question? Well, you need to perform the reverse to backtrack to the canonical sum of products (sum of min terms). In my example, we'd say:

f(a, b, c) = ab

For every omitted variable, you'd multiply in (that variable + that variable') and then distribute:

f(a, b, c) = ab = ab(c + c') = abc + abc'

another example:

f(a, b, c, d) = ab = ab(c + c')(d + d') = abcd + abcd' + abc'd + abc'd'

And to answer the second part of your question, to arrive to a minimal sum of products, you need to do what i first described: find redundancies, undistribute, and eliminate them. Google k-map for a quick, visual approach to minimizing sums of products.