When using a K-Map to determine the minimal form of a function, do we have to us

Question

When using a K-Map to determine the minimal form of a function, do we have to use don't-cares? I ask because my answer is different for both. Please view the following links to see the difference.

If this first image, I use the don't-cares in the grouping: https://gyazo.com/3d64169da499686edb1c609e4604fbe7

In this second image, I do not use the don't cares in the grouping: https://gyazo.com/e71200e1001021924a6162b4cec59a85

In the first one I have 3 groups and in the second I have 2. So I guess the second one would be the minimal, but I'm just not sure if we need to use don't-cares or not.

Explanation / Answer

Don't cares are the conditions for which we the designer don't care what the output is. These are those inputs in your truth table for which the output is irrelevant.

Now in this case adding don't cares is increasing the count of the function and therefore we should remove it. Don't care can be included or excluded in the K-map depending upon whether they simply your final design/function. In this case since it is not doing the same you can remove them.

The first image is fine and that should be the solution.

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