I have a K-Map for a given function and need to figure out the minimal form. This map involves don't-cares. My question is: Do I need to use the don't-cares in my minimal form. I will show you why I have this question.
If I use the don't-cares, then the resulting K-Map I get is this: https://gyazo.com/3d64169da499686edb1c609e4604fbe7
If I don't use the don't-cares, then the resulting K-Map I get is this: https://gyazo.com/e71200e1001021924a6162b4cec59a85
Which one of these would be the true minimal form? I guess my question is: if I have the don't-cares, do I need to use them?
In your example, the second form is smaller than the first one. Two terms are used rather than three. That is the minimum, as the four minterms in the example cannot be covered by less than two terms.
This simplification was possible by setting both don't care terms to 0. But there are other cases, when the don't cares can be chosen to be 1 to yield a miminum result.
Don't cares should not be ignored or omitted in general but chosen in such a way that the minterms can be covered with as few terms as possible.