Electronic – Karnaugh map: What values to combine

boolean-algebrakarnaugh map

I have obtained the Karnaugh diagram (pictured below) and now I'm trying to obtain the Boolean expression of K3 through this diagram. My inputs are Q1, Q2 and Q3. I'm trying to "group" 1's and X's together (where the X stands for the don't-care-variable). Now I'm not sure in what way I can group these 1's and X's. Can my groups overlap? Or should they be separate? I know the groups can only be the size of a power of 2.
Here are the options:

Original table: enter image description here

Option 1:
enter image description here

Option 2: enter image description here

Option 3: enter image description here

Can someone explain to me which "boxing" of values I should use to obtain my Boolean expression? Are my boxes allowed to overlap? Maybe there are other options for grouping this diagram?

Any help is appreciated! 🙂

Best Answer

The goal is to cover all '1's with blocks as large as possible. Overlapping boxes is permitted. All three of your options will result in a working solution, but none of them are optimal.

This problem can be solved with two blocks.

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