# Don't-Care terms to form largest region in K-map

Discussion in 'Homework Help' started by xEnOnn, Feb 13, 2011.

1. ### xEnOnn Thread Starter New Member

Feb 2, 2011
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I have attached a K-map to this post. In the picture, why shouldn't I use the region circled by me in orange when simplifying the SOP expression? Or should I? I thought I should make use of the "don't care" terms to maximise the regions as much as possible to make the final expression the simplest?

Also, in this case, when asked for the number of prime implicants, do I only count the ones I used in the simplified equation or do I also include the other variety of prime implicants that I did and didn't use in my final expression in my count?

Thanks!

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2. ### Georacer Moderator

Nov 25, 2009
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You don't have to use every prime implicant to reach a solution. Actually, the less prime implicants you use to build the final expression, the better, provided that they fully cover all the aces.

If I were you and had to solve that problem I would use the green square, your orange line, and the red rectangle of 2 elements. I wouldn't use the purple one as it adds nothing more towards simplifying the function. Instead, it adds another product without covering any previously uncovered ace.

After I used your orange line, I would use the full green square, even if we have already covered part of it, as it yields the term BD which is shorter that BCD.

I 'm not 100% sure about the next one, but I think that the prime implicants refer to the maximum possible sets you can create, not the combination of them. That said, I would answer that the prime implicants are 4.

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