Questions with Karnaugh Map grouping

I have a question about grouping. The Kmap is designed to simplify expression by grouping together adjacent cells containing 1’s.

Why are the RED circles not considered for groups 5 and 6?
w’xy’z + w’xyz - overlaps and 2^

wx’y’z’ + wx’yz’ - wraps around bottom and 2^

Rule 8 says fewest number of groups possible, but these still seem like two more valid groups to me.


Hi! Welcome to the community!

That is a great question. It does look like the two 1s that you circled could be a valid group. There are many possible ways to group the 1s in a k-map, and it is a good idea to find the groupings that result in the fewest total number of groups. This makes the simplification easier overall.

While your red group could be a valid group, it’s not necessary because the two 1s it includes are already included in other groups (one is in the blue group, and the other is in the purple group). You would only need to create more groups if you had additional 1s that were not already included in a group.

I hope this helps! Let us know if you have any more questions.

Okay, thanks!

I guess that confuses me because in other examples of solutions, groups overlap with other groups that already have 1’s in them. It seems helter-skelter to me if they are added as more groups or not. I guess it isn’t “clicking” yet.

Hmm…I guess another way to put it is, you can keep adding groups until you don’t have any more “ungrouped” 1s. If all of your 1s are already in groups, you’re done grouping, even if there are other possible groupings out there.

Awesome, thanks. That helped a ton!

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