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Online minimization of boolean functions
Online minimization of boolean functions
Input equation = ~((a+~(~bc~d))(~ab+~cd))
Truth table
| a | b | c | d | Output |
| 0 |
0 |
0 |
0 |
1 |
| 0 |
0 |
0 |
1 |
0 |
| 0 |
0 |
1 |
0 |
1 |
| 0 |
0 |
1 |
1 |
1 |
| 0 |
1 |
0 |
0 |
0 |
| 0 |
1 |
0 |
1 |
0 |
| 0 |
1 |
1 |
0 |
0 |
| 0 |
1 |
1 |
1 |
0 |
| 1 |
0 |
0 |
0 |
1 |
| 1 |
0 |
0 |
1 |
0 |
| 1 |
0 |
1 |
0 |
1 |
| 1 |
0 |
1 |
1 |
1 |
| 1 |
1 |
0 |
0 |
1 |
| 1 |
1 |
0 |
1 |
0 |
| 1 |
1 |
1 |
0 |
1 |
| 1 |
1 |
1 |
1 |
1 |
DNF (with ~) = ~a~b~c~d + ~a~bc~d + ~a~bcd + a~b~c~d + a~bc~d + a~bcd + ab~c~d + abc~d + abcd
DNF (with overline) = abcd + abcd + abcd + abcd + abcd + abcd + abcd + abcd + abcd
CNF (with ~) = (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 + c + ~d)
CNF (with overline) = (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 + c + d)
Minimal Form (with ~) = ~b~d + ~bc + a~d + ac
Minimal Form (with overline) = bd + bc + ad + ac
Karnaugh map
| cd |
cd |
cd |
cd |
| ab |
1 |
0 |
1 |
1 |
| ab |
0 |
0 |
0 |
0 |
| ab |
1 |
0 |
1 |
1 |
| ab |
1 |
0 |
1 |
1 |