I need some clarification on grouping the adjacent ones. Does it matter if I group them in 2,4,8 or 16 as long as the 1's are adjacent to each other? In the attached image, I grouped the 1's in three groups of 4. Is the goal always to group as many 1's as possible as long as they are mutiples of 2? Thanks in advance.

 

No, because 6 is a multiple of 2.

The bigger the group, the few factors in the term, which is the goal. You also want the fewest groups (and, hence, the fewest terms). This is unless you are trying to also eliminate static timing hazards.

 

No, because 6 is a multiple of 2.

The bigger the group, the few factors in the term, which is the goal. You also want the fewest groups (and, hence, the fewest terms). This is unless you are trying to also eliminate static timing hazards.

Ok. I've been working some problems on karnaugh mapping since reading your response and seem to be getting the hang of it. Thanks for your time.

 

Hopefully somewhere in your reading you have come across an explanation of just what a Karnaugh map is and why/how it works. The basic idea is that it is a graphical way of simplifying logic equations by exploiting the identity:

AB + AB' = A

As you move between any two adjacent cells in a K-map there is exactly one variable that is changing and so it is complemented in one cell and uncomplemented in the other cell. Since all of the other variables are unchanging, this means they can all be factored out giving you something of the form XY(Z+Z') = ZY.

That is why when you set up a K-map, all of the labels have to be in gray code order (only one variable changes at each step).