**Explain K-MAP and its significance. Explain 2-variables, 3-variables and 4-variables K-MAP.**

**Answer: –** The Karnaugh map or k-map is a graphical technique for simplifying Boolean function. The k-map in a two dimensional representation of a truth table it provides a simpler method for minimizing logic expressions. The map method is ideally suited for four or less variables. But it becomes cumbersome for five or more variable. A karnaugh map is a diagram consisting of squares. Each square of the map represent either min term or max term. Any logic expression can be written as either sum of product term or product of sum term which is also called sum of min term and product of max term respectively. Therefore a logic expression can be easily represented on a karnaugh map.

A KARNAUGGH map for n variables made up of 2^{n} squares. Each square designate a product term in Boolean expression. For product term which are present in the expression. In case of sum of product, 1s can be written in Present Square and in case of product of sum term, 0s can be written in Present Square. Blank Square or opposite square indicate. That then contains nothing.

We can construct KARNAUGH map in two different forms for sum of product term and for product of sum term. Because in sum of product contains zero as complement value and one as un-complement value similarly in the product of sum term we use 1 as complement and 0 as un-complemented value function of both sum of product and product of sum about same except that the complement and un-complement value.

**2 variable k-map: –** In the 2 variable k-map, four squares are constructed. Each square contains one term of expression with two variables. **A 2 variable k-map for SOP and POS form are as follows: –**

**3 variables k-map: –** In the three variable k-map, 8 square is required. The 3-variables k-map can content either horizontally or vertically. **An example of 3 variables k-map for SOP and POS form are as follows: –**

**4 variable k-map: –** In the 4 variable k-map, 16 square are required. **An example of 4 variable k-map for SOP and POS form are as follows: –**