Alte Quine Mc Cluskeys und Übungen.

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Re: Alte Quine Mc Cluskeys und Übungen.

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Code: Alles auswählen

        b a x   b a y
0       0 0 0   0 0 0
1       0 0 1   1 1 1
2       0 1 0   0 1 0
3       0 1 1   1 0 1
4       1 0 0   0 1 1
5       1 0 1   0 0 1
6       1 1 0   0 1 0
7       1 1 1   1 1 1



        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1




        b a x   b
1       0 0 1   1
3       0 1 1   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1




        b a x   b
Gruppe 1
1       0 0 1   1
Gruppe 2
3       0 1 1   1
Grupppe 3
7       1 1 1   1

        b a x   a
Gruppe 1
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2
6       1 1 0   1
Gruppe 3
7       1 1 1   1

        b a x   y
Gruppe 1
1       0 0 1   1
4       1 0 0   1
Gruppe 2
3       0 1 1   1
5       1 0 1   1
Gruppe 3
7       1 1 1   1




        b a x   b
Gruppe 1
1       0 0 1   1
Gruppe 2
3       0 1 1   1
Grupppe 3
7       1 1 1   1

1;3     0 - 1
3;7     - 1 1

b := (not b and x) or (a and x)

        b a x   a
Gruppe 1
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2
6       1 1 0   1
Gruppe 3
7       1 1 1   1

1       0 0 1
2;6     - 1 0
4;6     1 - 0
6;7     1 1 -

a := (not b and not a and x) or (a and not x) or (b and not x) or (b and a)

        b a x   y
Gruppe 1
1       0 0 1   1
4       1 0 0   1
Gruppe 2
3       0 1 1   1
5       1 0 1   1
Gruppe 3
7       1 1 1   1


1;5     1 0 -
1;3     0 - 1
4;5     - 0 0
5;7     1 - 1
3;7     - 1 1


1;5     1 0 -
1;3     0 - 1
5;7     1 - 1
3;7     - 1 1
4;5     - 0 0

1;3;5;7 - - 1

            1   3   4   5   7
1;5         *           *
1;3         *   *
5;7                     *   *
3;7             *           *
4;6                 *   *


            1   3   4   5   7
1;5         *           *
3;7             *           *
4;6                 *   *

y := (b and not a) or (a and x) or (not a and not x)
b := (not b and x) or (a and x)
a := (not b and not a and x) or (a and not x) or (b and not x) or (b and a)

Code: Alles auswählen

        b a x   b a y
0       0 0 0   0 0 1
1       0 0 1   1 1 0
2       0 1 0   0 1 0
3       0 1 1   1 0 1
4       1 0 0   0 0 0
5       1 0 1   1 0 0
6       1 1 0   0 0 0
7       1 1 1   1 0 1


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   0

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1





        b a x   b
1       0 0 1   1
3       0 1 1   1
5       1 0 1   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
2       0 1 0   1

        b a x   y
0       0 0 0   1
3       0 1 1   1
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1;3     0 - 1
1;5     - 0 1
3;7     - 1 1
5;7     1 - 1

1;3     0 - 1
5;7     1 - 1
1;5     - 0 1
3;7     - 1 1

1;3;5;7     - - 1
1;5;3;7     - - 1

b := x


        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1

a := (not b and not a and x) or (not b and a and not x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

0       0 0 0
3;7     - 1 1

y := (not b and not a and not x) or (a and x)




b := x
a := (not b and not a and x) or (not b and a and not x)
y := (not b and not a and not x) or (a and x)

Code: Alles auswählen

        b a x   b a y
0       0 0 0   1 1 1
1       0 0 1   0 1 0
2       0 1 0   0 0 1
3       0 1 1   1 1 0
4       1 0 0   0 0 1
5       1 0 1   1 1 1
6       1 1 0   1 0 1
7       1 1 1   0 1 1


        b a x   b
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1




        b a x   b
0       0 0 0   1
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

        b a x   a
0       0 0 0   1
1       0 0 1   1
3       0 1 1   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1



        b a x   b
Gruppe 0
0       0 0 0   1
Gruppe 2
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

b := (not b and not a and not x) or (not b and a and x) or (b and not a and x) or (b and a and not x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Grupe 3:
7       1 1 1   1

0;1     0 0 -
1;3     0 - 1
5;7     1 - 1
1;5     - 0 1
3;7     - 1 1

0;1         0 0 -
1;3;5;7     - - 1
1;5;3;7     - - 1

a := (not b and not a) or x


        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
0;4     - 0 0
2;6     - 1 0
4;5     1 0 -
4;6     1 - 0
5;7     1 - 1
6;7     1 1 -


Gruppe 2:
6;7     1 1 -
Gruppe 1:
4;5     1 0 -

6;7;4;5     1 - -

Gruppe 0:
0;2     0 - 0
Gruppe 1:
4;6     1 - 0
Gruppe 2:
5;7     1 - 1

0;2;4;6     - - 0
4;6;5;7     1 - -

Gruppe 0:
0;4     - 0 0
Gruppe 1:
2;6     - 1 0

0;4;2;6     - - 0

y := not x or b



b := (not b and not a and not x) or (not b and a and x) or (b and not a and x) or (b and a and not x)
a := (not b and not a) or x
y := not x or b

Code: Alles auswählen

        b a x   b a y
0       0 0 0   0 0 0
1       0 0 1   1 0 0
2       0 1 0   0 0 1
3       0 1 1   1 1 0
4       1 0 0   0 0 1
5       1 0 1   0 1 0
6       1 1 0   1 0 1
7       1 1 1   0 1 1


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1




        b a x   b
1       0 0 1   1
3       0 1 1   1
6       1 1 0   1

        b a x   a
3       0 1 1   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
2       0 1 0   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

        b a x   a
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1




        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

1;3     0 - 1
6       1 1 0

b := (not b and x) or (b and a and not x)

        b a x   a
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

3;7     - 1 1
5;7     1 - 1

a := (a and x) or (b and x)


        b a x   y
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

2;6     - 1 0
4;6     1 - 0
6;7     1 1 -

y := (a and not x) or (b and not x) or (b and a)


b := (not b and x) or (b and a and not x)
a := (a and x) or (b and x)
y := (a and not x) or (b and not x) or (b and a)

Code: Alles auswählen

        b a x   b a y
0       0 0 0   0 0 1
1       0 0 1   1 1 1
2       0 1 0   1 0 1
3       0 1 1   0 1 0
4       1 0 0   1 1 1
5       1 0 1   0 1 1
6       1 1 0   0 0 0
7       1 1 1   1 0 0


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0



        b a x   b
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

b := (not b and not a and x) or (not b and a and not x) or (b and not a and not x) or (b and a and x)

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1


1;3     0 - 1
1;5     - 0 1
4;5     1 0 -

        1   3   4   5
1;3     *   *
1;5     *           *
4;5             *   *

        1   3   4   5
1;3     *   *
4;5             *   *

a := (not b and x) or (b and not a)


        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1

0;1     0 0 -
0;2     0 - 0
0;4     - 0 0
1;5     - 0 1
4;5     1 0 -


0;1     0 0 -
4;5     1 0 -
0;2     0 - 0
0;4     - 0 0
1;5     - 0 1


0;1;4;5     - 0 -
0;4;1;5     - 0 -
0;2         0 - 0

y := (not a) or (not b and not x)


b := (not b and not a and x) or (not b and a and not x) or (b and not a and not x) or (b and a and x)
a := (not b and x) or (b and not a)
y := (not a) or (not b and not x)

Code: Alles auswählen

        b a x   b a y
0       0 0 0   0 1 0
1       0 0 1   0 0 1
2       0 1 0   0 1 0
3       0 1 1   1 1 1
4       1 0 0   0 0 0
5       1 0 1   1 0 0
6       1 1 0   0 1 1
7       1 1 1   1 1 1


        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1



        b a x   b
3       0 1 1   1
5       1 0 1   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
3       0 1 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
1       0 0 1   1
3       0 1 1   1
6       1 1 0   1
7       1 1 1   1



        b a x   b
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1





        b a x   b
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

2;7     - 1 1
5;7     1 - 1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 1
2;3     0 1 -
2;6     - 1 0
3;7     - 1 1
6;7     1 1 -


2;3     0 1 -
6;7     1 1 -
0;2     0 - 1
2;6     - 1 0
3;7     - 1 1

2;3;6;7     - 1 _
2;6;3;7     - 1 -
0;2         0 - 1

        b a x   y
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

1;3     0 - 1
3;7     - 1 1
6;7     1 1 -

        1   3   6   7
1;3     *   *
3;7         *       *
6;7             *   *

        1   3   6   7
1;3     *   *
6;7             *   *













        b a x   b
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

2;7     - 1 1
5;7     1 - 1


b := (a and x) or (b and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 1
2;3     0 1 -
2;6     - 1 0
3;7     - 1 1
6;7     1 1 -


2;3     0 1 -
6;7     1 1 -
0;2     0 - 1
2;6     - 1 0
3;7     - 1 1

2;3;6;7     - 1 _
2;6;3;7     - 1 -
0;2         0 - 1

a := a or (not b and x)

        b a x   y
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

1;3     0 - 1
3;7     - 1 1
6;7     1 1 -

        1   3   6   7
1;3     *   *
3;7         *       *
6;7             *   *

        1   3   6   7
1;3     *   *
6;7             *   *

y := (not b and x) or (b and a)


b := (a and x) or (b and x)
a := a or (not b and x)
y := (not b and x) or (b and a)

Code: Alles auswählen

        b a x   b a y
0       0 0 0   0 1 1
1       0 0 1   0 0 1
2       0 1 0   1 0 0
3       0 1 1   0 1 0
4       1 0 0   0 0 1
5       1 0 1   1 1 0
6       1 1 0   0 0 0
7       1 1 1   0 1 1



        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1




        b a x   b
Gruppe 2:
2       0 1 0   1
5       1 0 1   1

y := (not b and a and not x) or (b and not a and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0       0 0 0
3;7     - 1 1
5;7     1 - 1

a := (not b and not a and not x) or (a and x) or (b and x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

0;1     0 0 -
0;4     - 0 0
7       1 1 1 

y := (not b and not a) or (not a and not x) or (a and b and c)


y := (not b and a and not x) or (b and not a and x)
a := (not b and not a and not x) or (a and x) or (b and x)
y := (not b and not a) or (not a and not x) or (a and b and c)
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