Answer to Question #201529 in Discrete Mathematics for siddharth

Question

Discuss Karnaugh map with one, two, three and four

variables

Answer 1

One variable: 1 variable K map is not possible. For K-map to minimize atleast 2 variables are required.

One variable function can be easily minimized with the help of Boolean. There is no need of K-map

Two Variable: In 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 :

Three Variable: In the three variable K-map 8 squares are required. The 3 variable K-map can content either horizontally or vertically. An example of 3 variables k-map for SOP and POS form are as follows:

Four Variable K-map : In the 4 Variables K-map 16 squares are required. An example of 4 variable k-map for SOP and POS form are as follows:

Steps to solve expression using K-map:

1. Select K-map according to the number of the variables.
2. Identify minterms or maxterms as given in the problem.
3. For SOP put 1's in blocks of K-map respective to minterms(0's elsewhere)
4. For POS put 0's in blocks of K-map respective to maxterms(1's elsewhere)
5. Make rectangular groups containing total terms in power of two like 2,4,8...(except 1) and try to cover as many elements as you can in one group.
6. From the groups made in step 5 , find the product terms and sum them up for SOP form.