karnaugh-map

Karnaugh map group sizes


Full disclosure, this is for an assignment I don't think I'm looking for spoon feeding, more so just a general question. Am a I allowed to break that into a group of 8 and 2 groups of 4, or do all group sizes have to be equal, ie 4 groups of 4

1 0 1 1

0 0 0 0

1 1 1 1

1 1 1 1

Sorry if this is obvious, but my searches haven't been explicit and my teacher was quite vague. Thanks!


Solution

  • TL;DR: Groups don't have to be equal in size.

    Let see what happens if, in your case, you take 11 groups of one. Then you will have an equation of eleven terms. (ie. case_1 or case_2 or... case_11).

    By making big group, in your case 1 group of 8 and 2 groups of 4, you will have a very short and simplified equation like: case_group_8 or case_group_4_1 or case_group_4_2.

    Both grouping are correct (we took all the one in the map) but the second is the most optimized. (i.e. you cannot simplified more)

    Making 4 groups of 4 will bring you an equation that can be simplified more.

    The best way now is for you to try both grouping (all 4 vs 8/4/4) and see the output result.