# The Karnuagh Map

Posted on at

Karnaugh map is a systematic method for simplifying Boolean expression, where SOP and POS ( sum of product n product of sum). The effectiveness of Algebra depends upon simplification with all the laws, rules, and theorems of Boolean  and our ability to apply them. The karnaugh map, on the other hand , basically provide a “cookbook” method for simplification.

A Karnaugh map is similar because it presents all possible values of input variables and the resulting output for each value. Instead of being organized  into columns and rows like a truth table, the Karnaugh map  is an array of cells in which each cell represent binary value of input of input variables .The cells are arranged in away so that simplification of a given expression is simply a matter of properly grouping the cells. Karnaugh  map can be used for expression with two, four, five or six variables. Another  method, which is beyond our scope is  the Quine-McClusky method can be used for higher numbers of variables.

The number of cells in a Karnuagh map is equal to total number of possible input variable combinations as in number of rows in truth table. For three variables number of cells is 2^3=8. For four variables ,  the number of cells is 2^4 = 16.

For example Karnaugh Map For variable is asquare as :