# Karnaugh map or K Map

## Karnaugh-map or K-map

The Boolean theorems and De-Morgan’s theorems are useful in manipulating the logic expression. We can realize the logical expression using gates. The no. of logic gates required for the realization of a logical expression should be reduced to minimum possible value by K-map method.This method can be by two way

### Sum of Products (SOP) Form

It is in the form of sum of three terms AB,AC,BC with each individual term is product of two variable. Say A.B or A.C etc. Therefore such expression are known as expression in SOP form. The sum and products in SOP form are not the actual additions or multiplications. In fact they are the OR and AND functions. In SOP form, 0 is represent for bar and 1 is represent for unbar. SOP form is represented by .

Example of SOP is as follows.

### Product of Sums (POS) Form

It is in the form of product of three terms (A+B),(B+C) and (A+C) with each term is in the form of sum of two variables. Such expression are said to be in the product of sums (POS) form. In POS form, 0 is represent for unbar and 1 is represent for bar. POS form is represented by .

Example of POS is as follows.