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I am having trouble simplifying logical expressions to a much simpler form, can someone provide me some insight on how to approach the problem?

Let's assume i have the following expression: $ABCD + A\bar{B}CD$.

I am aware of the De Morgan's law, but not sure how to apply them in this case.

Thank you!

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  • $\begingroup$ Define "simpler form"... what is "simple" usually depends quite a bit on intended use, and moreover has strong "taste" components... $\endgroup$ – vonbrand Dec 19 '15 at 3:30
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What kind of simplification are you looking for ?

In the case you've given, $ABCD+A\bar{B}CD= ACD(B+\bar{B}) = ACD $.

In any case, this is a set of laws of Boolean algebra that might be helpful.

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Starting with an expression in canonical normal form, you can simplify it by applying normal algebraic methods ABCD + ABbarCD = ABCD(1 + bar) = ABCD or in less obvious cases using a Karnaugh map.

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    $\begingroup$ The Quine-McCluskey algorithm is more efficient than Karnaugh maps if you want to implement it as a program. $\endgroup$ – Pseudonym Dec 16 '15 at 23:07

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