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Online minimization of boolean functions
Online minimization of boolean functions
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 |
0 |
| 0 |
1 |
0 |
0 |
0 |
| 0 |
1 |
0 |
1 |
1 |
| 0 |
1 |
1 |
0 |
0 |
| 0 |
1 |
1 |
1 |
1 |
| 1 |
0 |
0 |
0 |
1 |
| 1 |
0 |
0 |
1 |
0 |
| 1 |
0 |
1 |
0 |
1 |
| 1 |
0 |
1 |
1 |
0 |
| 1 |
1 |
0 |
0 |
1 |
| 1 |
1 |
0 |
1 |
1 |
| 1 |
1 |
1 |
0 |
1 |
| 1 |
1 |
1 |
1 |
0 |
DNF (with ~) = ~a~b~c~d + ~a~bc~d + ~ab~cd + ~abcd + a~b~c~d + a~bc~d + ab~c~d + ab~cd + abc~d
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)
Some minimal forms exist.
Minimal Form (with ~) =
~abd + ~b~d + a~d + b~cd
~abd + ~b~d + a~d + ab~c
Minimal Form (with overline) =
abd + bd + ad + bcd
abd + bd + ad + abc
Karnaugh map
| cd |
cd |
cd |
cd |
| ab |
1 |
0 |
0 |
1 |
| ab |
0 |
1 |
1 |
0 |
| ab |
1 |
1 |
0 |
1 |
| ab |
1 |
0 |
0 |
1 |