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Need help have no idea the thought process in doing this kind of simplification. ! - Denotes NOT Lets say I have !((A+B) * (A+!B)) I need to simplify that using all rules except absortion.
I know it is A * !B + !A * B but I need to know the process to get there. What is a good place to start. I do several different things but I never come up with the right answer.

Bill the Lizard
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Doug
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    What do you mean by "simplify"? Someone could tell you how to obtain a conjunctive normal form, or a disjunctive normal form. On your example, it seems that you are looking for the latter, but the DNF is not always the simplest. On some examples it is much larger than the original. – Pascal Cuoq Feb 12 '10 at 16:28
  • If the DNF is what you want to obtain, a link: http://en.wikipedia.org/wiki/Disjunctive_normal_form – Pascal Cuoq Feb 12 '10 at 16:30

4 Answers4

5

Karnaugh maps should be a good start.

dirkgently
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  • While a Karnaugh map would certainly show the equivalence, he states in his assignment he needs to apply a series of rules to show the transformation. – danben Feb 12 '10 at 16:28
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    @danben: Really? I had read that as "he is not able to formulate how to apply the rules in a logical fashion to reach a result always." – dirkgently Feb 12 '10 at 16:33
  • "I need to simplify that using all rules except absortion.", where "that" refers to the expression he posted. – danben Feb 12 '10 at 17:55
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As a process of simplification use De Morgan's Law to move the NOT operator into the parenthesis.

So it would be 

!((A+B) * (A+!B)) = !(A+B) + !(A+!B)

The next step (again use De Morgan's Law) after this would lead to your answer.

I hope this helps.

cheers

Arnkrishn
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  • That's what I said -- about 2 minutes earlier. Is this really a better answer to a **homework** question? Give him a hint, don't solve it for him. – tvanfosson Feb 12 '10 at 16:44
  • ends up being !A*!B + !A*B. None of the rules look like I'm going to be able to get an A out of there. am I not using De Morgan's rule right? I have it cancel out the ! on the one B, but it makes the A's a NOT when only one is suppose to be a NOT. – Doug Feb 12 '10 at 16:46
  • @Doug - !A*!B + !A*B is correct. if that's not the answer you're looking for, then either your problem or your answer has a typo. – mbeckish Feb 12 '10 at 17:37
  • @tvanfosson - Just thought of giving the first step and the means (De Morgan's Law) to solve it all together. May be, I should have restrained from passing on the 1st step. – Arnkrishn Feb 12 '10 at 20:01
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Try repeating applications of DeMorgan's Law.

tvanfosson
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Re: "What is a good place to start" - use a reference for boolean laws. Here is one that I found: http://www.laynetworks.com/Boolean%20Algebra.htm

Look through the laws and see which ones can be applied; then pick the one that looks most like it is a step in the right direction.

With practice you will learn to be able to intuit the right laws to select; in the meantime you will need to hunt and peck a little.

danben
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