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