karnaugh-map

Simplify boolean function with k-map


I have a function who outputs 1 when the four bit input represents a multiple of 3 in a complement-two style notation. The truth table for this function should be:

x y z t | f 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 - 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0

Then I construct a k-map to get the min-POS:

POS

POS Grouping

Problem here is that I have two option which I referenced with the blue/green color; and so a question arise: Are both okay? Is it normal that a k-maps gives more-than-one-way to simplify an expression?


Solution

  • Sorry that you are getting this reply so late. For the blue and green you can do one of them or you can do both of them in your circling. The kmap allows you to overlap the zeros in your map.

    And yes, it is normal for kmaps to give you more than one to simplify an expression. I hope I understood your question correctly.