CODEWITHSUNDEEP
boolean-logicsimplification
Chris
Chris

Reputation: 1705

Boolean simplification with some known term combinations

I am doing boolean simplification using Quine-McCluskey which works well.

However, I now need to perform the simplification with some known term combinations.

For example, I want to simplify:

(A+B)C

If I know that:

A+B == true

then this simplifies to:

C

Or if I know that:

BC == false

then it simplifies to

AC

Is there an algorithm that can simplify boolean expressions given a list of known terms?

Upvotes: 2

Views: 232

Answers (1)

Chris
Chris

Reputation: 1705

I've discovered a nice solution to this problem.

Quine-McCluskey is able to handle a truth-table where some of the terms are marked as "don't care", which means that the term will never occur, so the minimized expression can return true or false.

For example:

A B result
0 0 0
0 1 don't care
1 0 don't care
1 1 con't care

It can clearly be seen that the above function can be minimized to just return 'false', as that is the only result that we care about.

So to deal with known terms, all that has to be done is set the result to "don't care" for any terms in the truth table where a known term evaluates to false. The Quine-McCluskey algorithm then generates the minimized function taking the known terms into account.

For example, if we have a function of A and B, and we know that A == false, then any line on the truth-table where A is true can be marked as "don't care" because we know it will never occur.

Upvotes: 2

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