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Discuss Karnaugh map with one, two, three and four variables
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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:
- Select K-map according to the number of the variables.
- Identify minterms or maxterms as given in the problem.
- For SOP put 1's in blocks of K-map respective to minterms(0's elsewhere)
- For POS put 0's in blocks of K-map respective to maxterms(1's elsewhere)
- 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.
- From the groups made in step 5 , find the product terms and sum them up for SOP form.