Quine Mc Cluskey and Automat

 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    0
 8 1 0 0 0    0
 9 1 0 0 1    1
10 1 0 1 0    0
11 1 0 1 1    0
12 1 1 0 0    1
13 1 1 0 1    1
14 1 1 1 0    0
15 1 1 1 1    0


a    0 0 0 0 0    0
b    1 0 0 0 1    0
c    2 0 0 1 0    0
d    3 0 0 1 1    1
e    4 0 1 0 0    1
f    5 0 1 0 1    1
g    6 0 1 1 0    1
h    7 0 1 1 1    0
i    8 1 0 0 0    0
j    9 1 0 0 1    1
k   10 1 0 1 0    0
l   11 1 0 1 1    0
m   12 1 1 0 0    1
n   13 1 1 0 1    1
o   14 1 1 1 0    0
p   15 1 1 1 1    0


d    3 0 0 1 1    1
e    4 0 1 0 0    1
f    5 0 1 0 1    1
g    6 0 1 1 0    1
j    9 1 0 0 1    1
m   12 1 1 0 0    1
n   13 1 1 0 1    1


 3 0 0 1 1    1
 4 0 1 0 0    1
 5 0 1 0 1    1
 6 0 1 1 0    1
 9 1 0 0 1    1
12 1 1 0 0    1
13 1 1 0 1    1

Gruppe 1:
 4 0 1 0 0    1
Gruppe 2:
 3 0 0 1 1    1
 5 0 1 0 1    1
 6 0 1 1 0    1
 9 1 0 0 1    1
12 1 1 0 0    1
Gruppe 3:
13 1 1 0 1    1

4;5         0 1 0 -
4;6         0 1 - 0
4;12        - 1 0 0
3           0 0 1 1
5;13        - 1 0 1
6           0 1 1 0
9;13        1 - 0 1
12;13       1 1 0 -


4;5         0 1 0 -
12;13       1 1 0 -
4;6         0 1 - 0
9;13        1 - 0 1
5;13        - 1 0 1
4;12        - 1 0 0
3           0 0 1 1
6           0 1 1 0

Gruppe 1:
4;5         0 1 0 -
Gruppe 2:
12;13       1 1 0 -

4;6         0 1 - 0

9;13        1 - 0 1

Gruppe 1:
4;12        - 1 0 0
Gruppe 2:
5;13        - 1 0 1

3           0 0 1 1
6           0 1 1 0


Gruppe 1:
4;5         0 1 0 -
Gruppe 2:
12;13       1 1 0 -

4;5;12;13   - 1 0 -

4;6         0 1 - 0

9;13        1 - 0 1

Gruppe 1:
4;12        - 1 0 0
Gruppe 2:
5;13        - 1 0 1

4;12;5;13   - 1 0 -

3           0 0 1 1
6           0 1 1 0


4;5;12;13   - 1 0 -
4;6         0 1 - 0
9;13        1 - 0 1
4;12;5;13   - 1 0 -
3           0 0 1 1
6           0 1 1 0


4;5;12;13   - 1 0 -
4;6         0 1 - 0
9;13        1 - 0 1
3           0 0 1 1
6           0 1 1 0

Minimale Restueberdeckung

            3   4   5   6   9   12  13
4;5;12;13       *   *           *   *
4;6             *       *
9;13                        *   *   *
3           *
6                       *


            3   4   5   6   9   12  13
4;5;12;13       *   *           *   *
4;6             *       *
9;13                        *   *   *
3           *

4;5;12;13       x2 and not x1
4;6             not x3 and x2 and not x0
9;13            x3 and not x1 and x0
3               not x3 and not x2 and x1 and x0

DNF:

y <= (x3 and not x1) or (not x3 and x2 and not x0) or (x3 and not x1 and x0) or (not x3 and not x2 and x1 and x0)