Groupings for K maps

Hi everyone!

Learning Challenge

I’m practicing the challenges on K-maps and for the practice " Boolean Algebra and Digital Logic Project 1" I’m really confused as to how the groupings work.

I understand that groups need to have the most # of members possible and that I need to have the least number of groups possible.

Question

The screenshots below are outline substitute groupings that would satisfy both least number of groupings and largest groups possible but they encompass different locations on the truth table.

**My question is, how do I know which grouping is the best when I have multiple options?

----In the screenshot below(1) why can’t I use the red group instead of group 2?(same size, same total number of groups):

In the screenshot below(2) why cant I use the RED group instead of the BLUE group?(same size, same total number of groups):

Great questions!

First, there are often several possible groupings that would be valid, as long as they follow the grouping rules. Often, the “best” grouping strategy is the one that forms the fewest number of largest groups, because that makes the simplification easier.

To specifically answer your questions:

  • In the top screenshot, the red grouping is not a valid option because the two 1s are not adjacent to each other. You cannot skip the 0 in between them to make a group. The blue G2 group is valid because the 1 on the top row and the 1 on the bottom row are technically adjacent to each other (wrapping around from the top of the K map to the bottom is OK).

  • In the bottom screenshot, the red and blue group options are both valid. I would recommend trying to complete the problem using the blue group, then try solving again using the red group, and see if one grouping or the other is easier to simplify. However, either approach should work!

Let me know if this raises any more questions. It’s great to see that you are analyzing these so closely!
Jesse

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Thanks a lot for your reply, that’s great help!

I have another question about diagrams, I was wondering where are the 0s and 1s in the example below from? and also why are there multiple connections going out of some of them while some others do not have any connections?(and why do we have them on the diagram if there are no connections going out)

ps- I’m guessing they have to do with the number of values present on the truth table for this example:w, x, y, z however I still dont understand how the assignment of 0 or 1 is decided

Hi, great question!

The 0s and 1s are basically the “given” values for this problem. Take a look at this discussion from a few months ago in which Brendan does a nice job of explaining how it works.

Jesse

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Thanks a lot! so from what I understood those 0s and 1s are not based on anything and will be given to us for each diagram.

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Yes, they will always be given to you!