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Online minimization of boolean functions
Online minimization of boolean functions
bin ( 4 ) 0000011101110110
Truth table
| a | b | c | d | Output |
| 0 |
0 |
0 |
0 |
0 |
| 0 |
0 |
0 |
1 |
0 |
| 0 |
0 |
1 |
0 |
0 |
| 0 |
0 |
1 |
1 |
0 |
| 0 |
1 |
0 |
0 |
0 |
| 0 |
1 |
0 |
1 |
1 |
| 0 |
1 |
1 |
0 |
1 |
| 0 |
1 |
1 |
1 |
1 |
| 1 |
0 |
0 |
0 |
0 |
| 1 |
0 |
0 |
1 |
1 |
| 1 |
0 |
1 |
0 |
1 |
| 1 |
0 |
1 |
1 |
1 |
| 1 |
1 |
0 |
0 |
0 |
| 1 |
1 |
0 |
1 |
1 |
| 1 |
1 |
1 |
0 |
1 |
| 1 |
1 |
1 |
1 |
0 |
DNF (with ~) = ~ab~cd + ~abc~d + ~abcd + a~b~cd + a~bc~d + a~bcd + ab~cd + abc~d
DNF (with overline) = 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) (~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) (a + b + c + d)
Some minimal forms exist.
Minimal Form (with ~) =
a~bc + a~cd + bc~d + ~abd
ac~d + a~bd + ~abc + b~cd
Minimal Form (with overline) =
abc + acd + bcd + abd
acd + abd + abc + bcd
Karnaugh map
| cd |
cd |
cd |
cd |
| ab |
0 |
0 |
0 |
0 |
| ab |
0 |
1 |
1 |
1 |
| ab |
0 |
1 |
0 |
1 |
| ab |
0 |
1 |
1 |
1 |