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# Karnaugh map

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### Karnaugh map

1. 1. Karnaugh Map<br />
2. 2. Introduction<br />A karnaugh map is a visual display of the fundamental products needed for a sum of products solution.<br />By using this map we can easily simplify the Boolean equations in sum of product form.<br />
3. 3. Two – variable map Truth table<br />
4. 4. Karnaugh map<br />B<br />A<br />B<br />10<br />11<br />03<br />02<br />A<br />
5. 5. Explanation<br />The vertical column has A followed by , and the horizontal row B followed by .<br />Then take the combination of inputs which produce the output as 1.<br />A<br />B<br />
6. 6. Cont.,<br />In the given truth table, the output is 1 at and <br /> input combinations.<br />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.<br />B<br />A<br />B<br />A<br />A<br />B<br />A<br />B<br />
7. 7. Three variable map Truth table<br />
8. 8. Karnaugh map<br />C<br />10<br />11<br />B<br />A<br />B<br />A<br />02<br />13<br />A<br />B<br />C<br />A<br />B<br />06<br />07<br />04<br />05<br />
9. 9. Explanation<br />The vertical column is labeled as , , , <br />This order is not a binary progress of 00,01,10 and 11.<br />A<br />B<br />A<br />B<br />A<br />B<br />A<br />B<br />
10. 10. Cont.,<br />In the karnaugh map the variables order are assigned in a sequence of only one variable changes from complemented to un complemented form.<br />The horizontal row is marked as and <br />C<br />C<br />
11. 11. Cont.,<br />The fundamental products for these 1 outputs are <br /> , and <br />Enter ‘1’ on these variables positions of the karnaugh map.<br />The remaining spaces are filled with 0’s.<br />C<br />A<br />B<br />C<br />A<br />B<br />A<br />B<br />C<br />
12. 12. Four variable map<br />Many digital systems process data in 4 bits (nibbles).<br />Some digital IC chips will work with nibbles like 0000, 0001 and so on.<br />
13. 13. Cont.,<br />For this reason, logic circuit are often designed to handle four input variables and their complements.<br />This is done by using 4 variable karnaugh map.<br />
14. 14. Four variable karnaugh map Truth Table<br />
15. 15. Cont.,<br />
16. 16. Karnaugh map<br />10<br />11<br />03<br />02<br />04<br />05<br />07<br />16<br />012<br />013<br />015<br />114<br />18<br />19<br />011<br />110<br />A<br />B<br />A<br />B<br />A<br />B<br />A<br />B<br />C<br />D<br />C<br />D<br />C<br />D<br />C<br />D<br />
17. 17. Explanation<br />The vertical column is , , and .<br />The horizontal row is , , and . <br />A<br />B<br />A<br />B<br />A<br />B<br />A<br />B<br />C<br />D<br />C<br />D<br />C<br />D<br />C<br />D<br />
18. 18. Cont.,<br />The output 1 is appeared at the input combinations of<br /> , , , ,<br /> , and <br />Enter ‘1’ on these spaces of the karnaugh map, and the remaining spaces are filled with 0’s.<br />C<br />D<br />A<br />B<br />C<br />D<br />A<br />B<br />C<br />D<br />A<br />B<br />C<br />D<br />A<br />B<br />C<br />D<br />A<br />B<br />C<br />D<br />A<br />B<br />C<br />D<br />A<br />B<br />
19. 19. The End<br /> …… Thank You ……<br />