Am I to the end of this Boolean Algebra Problem?

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Discussion Overview

The discussion revolves around the simplification of a Boolean algebra expression involving multiple variables. Participants explore different methods for simplification, including Boolean algebra axioms and Karnaugh maps, while seeking to determine the most reduced form of the expression.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents an initial Boolean expression and their simplification attempt, questioning if further reduction is possible.
  • Another participant mentions using a Karnaugh map and arrives at a different set of terms, prompting a question about the origin of a specific term in the first participant's result.
  • A participant references using Boolean algebra axioms for simplification and indicates they will provide further details later.
  • A subsequent reply corrects an earlier mistake in their K-map analysis, aligning their result with the first participant's outcome and emphasizes the utility of K-maps for simplification.
  • One participant expresses confidence in their mathematical approach but seeks a more compact form for practical purposes.

Areas of Agreement / Disagreement

Participants exhibit differing results from their simplification efforts, with some agreeing on a final expression while others initially disagree. The discussion reflects multiple approaches and results without a clear consensus on the simplest form.

Contextual Notes

Participants reference different methods and potential errors in their calculations, indicating that the simplification process may depend on the approach taken and the accuracy of the execution.

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Here's the problem:

a'b'c'd' + a'b'cd' + a'b'cd + ab'c'd' + abc'd'

I've gotten it down to:
ac'd' + b'c'd' + a'b'c

Having trouble coming up with a way to simplify it more...Is this as far as it can go?
Any help appreciated, thanks...
 
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I did a quick K-map, and got it down to 3 terms, but my terms are different from yours. I got 2 3-terms and one 4-term.

Did you use a Karnaugh map? Where did the ac'd' term come from, for example?
 
I used Boolean Algebra Axioms that I had learned in college to simplify it to the result that I got...

The lines are on the board at work, I'll try to update this thread with them tomorrow from work...

Thanks for the response...
 
berkeman said:
I did a quick K-map, and got it down to 3 terms, but my terms are different from yours. I got 2 3-terms and one 4-term.

Did you use a Karnaugh map? Where did the ac'd' term come from, for example?
I found an error in my quick K-map. I now get the same answer as you. For problems like this with up to 4 inputs, the K-map is the easiest way to see what the simplest answer is. Well, assuming you don't make an error like I did yesterday :blushing:
 
no problem...it happens...thanks for the update...i feel confident about the math, i just wanted it smaller to help out in a query that i was writing...
 

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