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Boolean Logic - Logic Project 1 - Problem 4

Learning Challenge

Boolean Algebra - Logic Project 1

Question

The solution provides four groups. The second group combines the four corners into a group. I grouped the two bottom on the left and right to create a group of four. All of my other groups were the same. The result is two different answers from what I can tell. My solution results in f(w,x,y,z) = w’x’+wz’+w’y+wx. Since these are both groups of four and all 1s are covered with these groups are they essentially equal within the function? How would this situation work on the test? I there a way to know which option to choose?

Also, the answer sheet has F(x, y, z) on all of the answers which include the variables w, x, y and z. Is there a reason the w is left out of the answer function?

What I’ve tried

I have reread the kmaps section and done some googling. I can’ seem to find anything on how determine which grouping to choose when there are multiple options.

Screenshots


Follow-up:
This video (lecture on kmaps) which I found on another post here talks through this problem a bit.

So let me revise my question a bit to: is my answer equally efficient since it contains the same number of groups and final terms? Are there things we should look for in the output functions to find efficiency there?

Hi Matthew,

In terms of efficiency, the general rule of thumb is to create a grouping strategy that includes the smallest number of largest groups - this will lead to less simplification needed in the end to get your answer down to the sum-of-products or product-of-sums format.

In terms of a test-taking strategy, you will ultimately need to choose the one correct answer out of a group of multiple choice options. If you solve the problem and do not see your answer listed in the answer choices, ask yourself the following questions to debug:

  • If I rearrange, or further simplify, can I get my answer to match one of the options?
  • If I use a different grouping strategy, will I get one of the options?

I hope this is helpful,
Jesse

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