Disjunktive Normalform f(x1,x2,x3) = ((not x1) and x2 and (not x3)) or (x1 and x2 and (not x3)) or (x1 and x2 and x3)
Kojunktive Normalform f(x1,x2,x3) = (x1 or x2 or x3) and (x1 or x2 or (not x3)) and (x1 or (not x2) or (not x3)) and ((not x1) or x2 or x3) and ((not x1) or x2 or (not x3))
5 0 1 0 1 1
7 0 1 1 1 1
9 1 0 0 1 1
11 1 0 1 1 1
13 1 1 0 1 1
14 1 1 1 0 1
15 1 1 1 1 1
Gruppe 2
5 0 1 0 1 1
9 1 0 0 1 1
Gruppe 3
7 0 1 1 1 1
11 1 0 1 1 1
13 1 1 0 1 1
14 1 1 1 0 1
Gruppe 4
15 1 1 1 1 1
5;7 0 1 - 1
5;13 - 1 0 1
9;11 1 0 - 1
9;13 1 - 0 1
7;15 - 1 1 1
11;15 1 - 1 1
13;15 1 1 - 1
14;15 1 1 1 -
(not x3 and x2 and x0) or
(x2 and not x1 and x0) or
(x3 and not x2 and x0) or
(x3 and not x1 and x0) or
(x2 and x1 and x0) or
(x3 and x2 and x0 or
(x3 and x1 and x0) or
(x3 and x2 and x1) or
5 7 9 11 13 14 15
5;7 * *
5;13 * *
9;11 * *
9;13 * *
7;15 * *
11;15 * *
13;15 * *
14;15 * *
* * * * * * *
5 7 9 11 13 14 15
5;7 * *
9;11 * *
13;15 * *
14;15 * *
(not x3 and x2 and x0) or (x3 and not x2 and x0) or (x3 and x2 and x0) or (x3 and x2 and x1)
c) KV-Diagramm
(not x2) and (not x1) (not x2) and x1 x2 and x1 x2 and (not x1)
00 01 11 10
(not x4) and (not x3) 00 1 0 0 0
(not x4) and x3 01 0 0 0 1
x4 and x3 11 1 0 1 0
x4 and (not x3) 10 1 0 1 0
x4 and x3 and (not x2) and (not x1), x4 and (not x3) and (not x2) and (not x1) => x4 and (not x2) and (not x1)
x4 and x3 and x2 and x1, x4 and (not x3) and x2 and x1 => x4 and x2 and x1
vereinfacht:
not x4 and not x3 and not x4 and not 3 or
not x4 and x3 and x2 and not x1 or
x4 and (not x2) and (not x1) or
x4 and x2 and x1
