Karnaugh maps are visual displays used to simplify Boolean equations in sum-of-products form by grouping variables. The document explains 2, 3, and 4 variable Karnaugh maps through examples, showing how to construct the maps from truth tables and identify product terms.

1. Karnaugh Map

2. IntroductionA karnaugh map is a visual display of the fundamental products needed for a sum of products solution.By using this map we can easily simplify the Boolean equations in sum of product form.

3. Two – variable map Truth table

4. Karnaugh mapBAB10110302A

5. ExplanationThe vertical column has A followed by , and the horizontal row B followed by .Then take the combination of inputs which produce the output as 1.AB

6. Cont.,In the given truth table, the output is 1 at and input combinations.Enter 1 in the spaces of and at the karnaugh map, because the corresponding outputs are high. The remaining spaces are entered with 0’s.BABAABAB

7. Three variable map Truth table

8. Karnaugh mapC1011BABA0213ABCAB06070405

9. ExplanationThe vertical column is labeled as , , , This order is not a binary progress of 00,01,10 and 11.ABABABAB

10. Cont.,In the karnaugh map the variables order are assigned in a sequence of only one variable changes from complemented to un complemented form.The horizontal row is marked as and CC

11. Cont.,The fundamental products for these 1 outputs are , and Enter ‘1’ on these variables positions of the karnaugh map.The remaining spaces are filled with 0’s.CABCABABC

12. Four variable mapMany digital systems process data in 4 bits (nibbles).Some digital IC chips will work with nibbles like 0000, 0001 and so on.

13. Cont.,For this reason, logic circuit are often designed to handle four input variables and their complements.This is done by using 4 variable karnaugh map.

14. Four variable karnaugh map Truth Table

15. Cont.,

16. Karnaugh map10110302040507160120130151141819011110ABABABABCDCDCDCD

17. ExplanationThe vertical column is , , and .The horizontal row is , , and . ABABABABCDCDCDCD

18. Cont.,The output 1 is appeared at the input combinations of , , , , , and Enter ‘1’ on these spaces of the karnaugh map, and the remaining spaces are filled with 0’s.CDABCDABCDABCDABCDABCDABCDAB

19. The End …… Thank You ……