2. Introduction A 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.
5. Explanation The 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. A B
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. B A B A A B A B
9. Explanation The vertical column is labeled as , , , This order is not a binary progress of 00,01,10 and 11. A B A B A B A B
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 C C
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. C A B C A B A B C
12. Four variable map Many 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.
16. Karnaugh map 10 11 03 02 04 05 07 16 012 013 015 114 18 19 011 110 A B A B A B A B C D C D C D C D
17. Explanation The vertical column is , , and . The horizontal row is , , and . A B A B A B A B C D C D C D C D
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. C D A B C D A B C D A B C D A B C D A B C D A B C D A B
