I'm trying to solve a very simple logic problem. We've been asked to construct a truth table and then a Karnaugh map based on the truth table to simplify the expression, then create a 2^nd truth table to verify that the simplified version (from the K Map) is logically equivalent. For some reason my two truth tables are not lining up so I must be doing something wrong.

 

The question says that the variables X Y Z each represent sensors, the state of M is true (=1) when one or more sensors are on. For a truth table this would be every row aside from the first one where all are equal to 0, correct?

 

Then my K Map gives me a group of 6 and a group of 2 which overlaps once with the 6, but the resulting expression is X'Z which is not equivalent.

 

This is driving me crazy because I know the problem is very simple. I'd really appreciate any advice here. Also if my question isn't clear I'd be more than happy to send a PDF with the problem and my solution I just can't post it here. Thanks in advance!!

I've been able to sort this problem out. Turns out I was illegally grouping on the Karnaugh map which was resulting in a false simplified expression. Don't you just hate it when you make silly mistakes and then continue doing it over and over again

Karnaugh Map is a special type of Truth Table, in order to resolve some boolean statements ...

 

http://en.wikipedia.org/wiki/Karnaugh_map

Edited January 26, 201213 yr by khaled