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 1 0
1       0 0 1   1 1 1
2       0 1 0   0 1 0
3       0 1 1   1 1 1
4       1 0 0   1 0 0
5       1 0 1   0 0 0
6       1 1 0   1 1 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   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

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

        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   0
7       1 1 1   0





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

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

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



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

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

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


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

1;3     0 - 1
4;6     1 - 0
3;7     - 1 1
6;7     1 1 -

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

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

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



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


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

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

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


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

            0   1   2   3   6   7
0;2;1;3     *   *   *   *
0;1;2;6     *   *   *       *
6;7                         *   *
3;7                     *       *

            0   1   2   3   6   7
0;2;1;3     *   *   *   *
6;7                         *   *

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


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

1;3     0 - 1

y := (not b and x)


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

Code: Alles auswählen

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


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

        b a x   a
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   0
7       1 1 1   0

        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   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1





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

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

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




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

        b a x   a
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

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



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

2;3     0 1 -
2;6     - 1 0
4;6     1 - 0

2;3     0 1 -
4;6     1 - 0
2;6     - 1 0

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


        b a x   a
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

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

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

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


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


2       0 1 0
5;7     1 - 1

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



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

Code: Alles auswählen

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




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

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




        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1

1       0 0 1
4;6     - 1 0

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

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

0;1     0 0 -
0;4     - 0 0
1;3     0 - 1
4;6     1 - 0
3;7     - 1 1 
6;7     1 1 -

0;1     0 0 -
6;7     1 1 -
1;3     0 - 1
4;6     1 - 0
3;7     - 1 1
0;4     - 0 0
                0   1   3   4   6   7
0;1             *   *
6;7                             *   *
1;3                 *   *
4;6                         *   *
3;7                     *           *
0;4             *           *

                0   1   3   4   6   7
0;1             *   *
6;7                             *   *
1;3                 *   *
4;6                         *   *

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

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

5;7     1 - 1

y := (b and x)


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

Code: Alles auswählen

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

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   1 1 0
3       0 1 1   0 1 0
4       1 0 0   1 1 0
5       1 0 1   0 0 1
6       1 1 0   1 0 0
7       1 1 1   1 1 1


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

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



        b a x   b
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;4     - 1 0
4;6     1 - 0
6;7     1 1 -

        2   4   6   7
2;4     *   *
4;6         *   *
6;7             *   *


        2   4   6   7
2;4     *   *
6;7             *   *

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

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


0;2     0 - 0
0;4     - 0 0
3;7     - 1 1
2;3     0 1 -

        0   2   3   4   7
0;2     *   *
0;4     *           *
3;7             *       *
2;3         *   *

        0   2   3   4   7
0;2     *   *
0;4     *           *
3;7             *       *

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


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

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

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


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

Code: Alles auswählen

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


        b a x   b
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   1
6       1 1 0   1
7       1 1 1   0

        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   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   1
6       1 1 0   0
7       1 1 1   1



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



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



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1


0;1     0 0 -
0;4     - 0 0
1;5     - 0 1
4;5     1 0 - 
4;6     1 - 0

Gruppe 0:
0;1     0 0 -
Gruppe 1:
4;5     1 0 - 

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


0;1;4;5     - 0 -
0;4;1;5     - 0 -
4;6         1 - 0

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

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

1;3;5;7     - - 1

a := x
        b a x   y
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

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

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

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

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




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

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

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

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

1;3     0 - 1
6       1 1 0

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


        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:
3       0 1 1   1
5       1 0 1   1

0;1     0 0 -
0;2     0 - 0
0;4     - 0 0 
1;3     0 - 1
2;3     0 1 -
1;5     - 0 1
4;5     1 0 -


1;5     - 0 1
0;4     - 0 0 
1;3     0 - 1
0;2     0 - 0
2;3     0 1 -
4;5     1 0 -
0;1     0 0 -



Gruppe 1:
1;5     - 0 1
Gruppe 0:
0;4     - 0 0 

1;5;0;4     - 0 -

Gruppe 1:
1;3     0 - 1
Gruppe 0:
0;2     0 - 0


1;3;0;2     0 - -

Gruppe 1:
2;3     0 1 -
4;5     1 0 -
Gruppe 0:
0;1     0 0 -

2;3;0;1     0 - -
4;5;0;1     - 0 -

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


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

Code: Alles auswählen

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

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



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

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

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



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

b := (not 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
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1

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

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

0;2;4;6     - - 0
0;4;6;2     - - 0

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

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

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

        0   1   2   5
0;1     *   *
0;2     *       *
1;5         *       *

        0   1   2   5
0;2     *       *
1;5         *       *

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



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

Code: Alles auswählen

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


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

        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   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   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   0




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

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

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





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

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




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


0;2     0 - 0
5       1 0 1
2;6     - 1 0

        0   2   5   6
0;2     *   *
5               *
2;6         *       *

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

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

1;5;3;7     - - 1

a := x


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


1;5     - 0 1
4;5     1 0 -
4;6     1 - 0

        1   4   5   6
1;5     *       *
4;5         *   *
4;6         *       *


        1   4   5   6
1;5     *       *
4;6         *       *

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



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