# Why do Karnaugh map work?

1. Aug 10, 2010

Why do Karnaugh map work? I don't understand how they work. If I follow the rules I get a minimized expression easily enough...it just seems like magic.

2. Aug 11, 2010

### Ir0nMan

Karnaugh Maps work because they utilize gray code to ensure that every two squares that share a side differ only by a negation on one term. This allows for the differing term to be neglected as it would create a sum of product for that looks similar to A'B'C'D+A'B'C'D', which can then be rewritten as A'B'C'(D+D'). You could probably deduce rather easily that the term in parentheses is equal to 1, since one of the two terms must always be true. since anything anded with 1 is simply itself, we can neglect writing the 1 and we are left with the term A'B'C'. This simplified form will represent a 1X2 box on a 4X4 Karnaugh map. Larger boxes can simply be viewed as further simplification of these intermediate terms.You may also want to take a look at the http://en.wikipedia.org/wiki/Quine%E2%80%93McCluskey_algorithm" [Broken] for minimization; it is based around the same principles.

Last edited by a moderator: May 4, 2017
3. Aug 11, 2010

### I_am_learning

While filling out the map, do you realize why each box is marked 0/1 ? Or do you just follow the rule and use the magic?