Grouping with Karnaugh Maps

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#1

Hello, I have a question pertaining to the Boolean Algebra and Digital Logic Learning Challenge.

While I have been practicing problems on the Boolean and Digital Logic Project 1 portion of this module, I happened to come across some confusion pertaining to grouping with Problem 4 of this project.

I was correct when I grouped the first and third rows, as well as when I grouped the upper-right square of 1s. However, my 4th group was supposed to be using the corners.

Instead, what I tried to do for this group was utilize a wrap around using the bottom two rows of 1s on the “00” and “10” miniterm columns, only to discover that this led to me obtaining an incorrect output for this specific group, and consequently, led me to getting the wrong answer overall. Pictured below is the Karnaugh Map for problem 4 and my grouping work underneath it:

IMG_20200708_214222599~2
IMG_20200708_214222599~23674×1805 1.51 MB

My questions are: Why is it incorrect to group wxy’z’ + w’x’y’z’ + wxyz’ + wx’yz’ in this problem? Also, are there specific ways you have to group the 1 values in Karnaugh Maps, or are you able to do so in any way, given that you follow all of the appropriate grouping rules (such as grouping the 2nd and 3rd row of 1s under the “11” and “10” miniterm columns in the above problem together as opposed to how it is done in the solution guide, which is how I did so in my 3rd group above)?

  • Matthew Hasan
#2

you can only group together outputs that are different by one variable. 0011 and 0001 are different by 2 variables in the wx portion, so they cannot be grouped together. You can only group together variables that touch each other or are connected through the wrap around principle, such as the 4 corners. wxy’z’ + w’x’y’z’ + wxyz’ + wx’yz’ is separated by w’xy’z’+ w’xy’z, which are incorrect inputs.

#3

Actually, what I was incorrectly attempting to wrap around is what I have now circled here. Even when I type this map into a Karnaugh Map solver, what I have circled is not considered a valid group. I’m not sure how these are different by more than one variable (which does seem to be the problem here, as it seems that there’s no way I’m not following the other grouping rules).

IMG_20200709_082307385~2
IMG_20200709_082307385~22080×1316 1.03 MB

#4

I have the same question, why does the above solution not work?

#5

I had a similar question as well. My intuition is that there can be multiple correct answers, and was able to confirm that with some Googling.