Electronic – Logic design k-map question

karnaugh map

K-map, d's represent don't care terms

Hi everyone I'm trying to minimize this boolean function F(A, B, C, D) = ∑m(7, 8, 9, 12, 13)
don't care terms(2, 3, 6, 10, 11, 14). My main question is about the row of don't care terms in the bottom row, do I include this as a group of 4 when minimizing? I assumed I should and got this product-of-sums AB'C + AC' + ACD' + A'C + B'C. I'm also, not that great at simplifying so do AC' and A'C cancell to get AB'C + ACD' + B'C? Any and all help is appreciated especially if you could give an explanation on how you simplified, thanks.

Best Answer

The point of minimizing a boolean function is that you want to output the same 0s and 1s with the smallest number of terms. A don't care can be either a 0 or a 1 - whichever makes the function simpler.

In your case, there's no reason to treat the entire CD' block of don't cares as 1s: if it doesn't make your SOP function simpler, don't add it.

I think the simplest SOP expression is AC' + A'C. Here's a picture of those two terms.

enter image description here

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