Karnaugh map(K-map)

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Conversion of Boolean fraction.


A Boolean expression can have two types.
*Sum of product.(SOP)
*product of sum(POS) 

 In the SOP Boolean expression,different product terms are combined with the addition operators, While POS Boolean expression different sum terms are combined with the product operator.The product in SOP Boolean expression are called minterms, while sum term in POS boolean expression are called maxterm.


Simplification of Boolean expression using K-MAP.

K-map is a technique of simplify the Boolean expression using graphical representation method. It simplifying the boolean expression by combining the similar expression and deleting the repeated variable.


Input A
Input B
Output Y
0
0
0
0
1
1
1
0
0
1
1
1

The 0's and 1's written at the top of K-map represent the value of the input variable,A nad B. The value inside the K-Map represent the output Y. Example- the lower left corner contains output corresponding to the input A=1 and B=0, moreover the decimal value can also written inside the block.




Number of cell in K-map is 2n, where n is number of variable.

 Step to slove expression using K-map.

 1.Select K-map according to the number of  variable.
2.Identify minterm or maxterm as given in problem.
3.For SOP put  1's in block of K- map respect to minterm.
4.For POS put 0's in block of K-map respect to maxterm.
5.Grouping two, four and eight adjacent.
Q simplify the following boolean expression using k-Map.
       













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