## Karnaugh Map Reduction

As reductions using the theorems of Boolean algebra are at times tricky, a graphical method of carrying out function reductions was developed by M. Karnaugh which makes logic reduction much easier. The Karnaugh map is shown below for three and four variable functions.

The maps above are organized so that groups like AB + AB' can be recognized and reduced (to A in this case) visually. To do this the truth table is mapped into the Karnaugh map and then squares of '1's are circled from the biggest square to the smallest square. It is important that the minimum number of circles is used and that the biggest possible squares is used in order to achieve a minimum reduction. When identifying squares, it must be kept in mind that the maps are actually three dimensional as shown below:

Example:

```
The truth table on the right has been mapped into the KMap
and then the squares of '1 's circled. Notice that the number
of '1's in a square is always a power of 2.

Writing out the term for each group yields the expression below:

F = A'BC'D + AC + B'D'

```