Karno is a Karnaugh map solver that works with any number of variables. It includes an algorithm to minimize a k-map and one to test the output SOP expression against all possible inputs for the function.
Given a 4-variables function having the following truth table
| Number | A | B | C | D | f(A, B, C, D) |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 2 | 0 | 0 | 1 | 0 | 0 |
| 3 | 0 | 0 | 1 | 1 | 1 |
| 4 | 0 | 1 | 0 | 0 | 1 |
| 5 | 0 | 1 | 0 | 1 | 1 |
| 6 | 0 | 1 | 1 | 0 | 1 |
| 7 | 0 | 1 | 1 | 1 | 1 |
| 8 | 1 | 0 | 0 | 0 | 0 |
| 9 | 1 | 0 | 0 | 1 | 0 |
| 10 | 1 | 0 | 1 | 0 | – |
| 11 | 1 | 0 | 1 | 1 | – |
| 12 | 1 | 1 | 0 | 0 | – |
| 13 | 1 | 1 | 0 | 1 | – |
| 14 | 1 | 1 | 1 | 0 | – |
| 15 | 1 | 1 | 1 | 1 | – |
The code to solve the corresponding k-map is:
// the first argument is the number of variables
// the second argument is on-set (each number represents the corresponding binary string)
// the third argument is the dc-set (each number represents the corresponding binary string)
var map = new KMap(4, new HashSet<long>() { 3, 4, 5, 6, 7 }, new HashSet<long>() { 10, 11, 12, 13, 14, 15 });
map.PrintCoverages(true); // Print only those with min cost
map.PrintTestResults(); // Test expression against all possible inputsThis code will produce the following output:
Coverage: 3
0011 - 0111 - 1011 - 1111 - Essential
0100 - 0101 - 0110 - 0111 - 1100 - 1101 - 1110 - 1111 - Essential
SOP: CD B
TEST: OK