1. ## Question about adjacency in K-maps?

I am looking at some k-maps and puzzled about grouping the adjacent cells. Pretend this is a 4 variable k-map of F(A,B,C,D) (sorry, I don't know of a better way to display them):

1100
1001
1001
1100

I see 3 groups:

1
100
1001
1001
1100

1100
1001
1001
1100

1100
1001
1001
1100

Are these 3 groups correct?

Also, pretend this is another 4 variable k-map:

0111
0111
0111
0111

How do you group these? It looks like one big group, but the size can't be 12 so I am stumped... Is it 3 groups, each containing the entire column?

2. There can be multiple ways of grouping in a k-map. For example, in your first example, you could also do it this way:

1100
1001
1001
1100

plus

1100
1001
1001
1100

plus

1100
1001
1001
1100

I doubt you can do it more efficiently than this.

As for your second example, couldn't you do a negation? That is, do the negation of

0111
0111
0111
0111

If you did that, that would be equivalent, via boolean algebra, to the following:

0111
0111
0111
0111

plus

0111
0111
0111
0111

Make sense?