x3 x2 x1 y
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1
x3 x2 x1 y
0 1 0 1
1 1 0 1
1 1 1 1
Die DNF lautet
y <= (not x3 and x2 and not x1) or
(x3 and x2 and not x1) or
(x3 and x2 and x1);
y <= not ( (x3 or not x2 or x1) and
(not x3 or not x2 or x1) and
(not x3 or not x2 or not x1)
);
Quine Mc Cluskey
x3 x2 x1 y
Gruppe 1:
0 0 1 0 1
Gruppe 2:
1 1 1 0 1
Gruppe 3:
2 1 1 1 1
0:1 - 1 0
1:2 1 1 -
Primimplikantentafel
0 1 2
0:1 * *
1:2 * *
Beide Primimplikanten sind Kernimplikanten
y <= (x2 and not x1) or
(x3 and x2);
y <= not ((not x2 or x1) and
(not x3 or not x2)
);
b)
Minimieren der Schaltfunktion
y <=
(x3 and x2 and not x1 and x0) or
(x3 and not x2 and x1 and x0) or
(x3 and not x2 and not x1 and x0) or
(not x3 and x2 and x0) or
(x3 and x2 and x1)
(x3 and x2 and not x1 and x0) or
(x3 and not x2 and x1 and x0) or
(x3 and not x2 and not x1 and x0) or
(not x3 and x2 and and x1 and x0) or
(not x3 and x2 and and not x1 and x0) or
(x3 and x2 and x1 and x0)
(x3 and x2 and x1 and not x0) or
1 1 0 1
1 0 1 1
1 0 0 1
0 1 1 1
0 1 0 1
1 1 1 1
1 1 1 0
Gruppe 2:
0 1 0 1
1 0 0 1
Gruppe 3:
0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0
Gruppe 4:
1 1 1 1
Gruppe 2:
0 0 1 0 1
1 1 0 0 1
Gruppe 3:
2 0 1 1 1
3 1 0 1 1
4 1 1 0 1
5 1 1 1 0
Gruppe 4:
6 1 1 1 1
0:2 0 1 - 1
0:4 - 1 0 1
1:3 1 0 - 1
1:4 1 - 0 1
2:6 - 1 1 1
3:6 1 - 1 1
4:6 1 1 - 1
5:6 1 1 1 -
5:6 1 1 1 -
0:2 0 1 - 1
1:3 1 0 - 1
4:6 1 1 - 1
1:4 1 - 0 1
3:6 1 - 1 1
0:4 - 1 0 1
2:6 - 1 1 1
5:6 1 1 1 -
Gruppe 2:
0:2 0 1 - 1
1:3 1 0 - 1
Gruppe 3:
4:6 1 1 - 1
0:2:4:6 - 1 - 1
1:3:4:6 1 - - 1
1:4 1 - 0 1
3:6 1 - 1 1
1:4:3:6 1 - - 1
0:4 - 1 0 1
2:6 - 1 1 1
0:4:2:6 - 1 - 1
5:6 1 1 1 -
1:4:3:6 1 - - 1
0:4:2:6 - 1 - 1
Primimplikantentafel
0 1 2 3 4 5 6
5:6 * *
1:4:3:6 * * * *
0:4:2:6 * * * *
Alles sind Kernimplikanten
y <= (x3 and x2 and x1) or
(x3 and x0) or
(x2 and x0);
(not x4 and x3 and x2 and not x1) or*
(x4 and not x3 and x2 and x1) or*
(x4 and x3 and x2 and x1) or*
(x4 and x3 and not x2 and x1) or*
(x4 and not x3 and not x2 and not x1) or
(not x4 and not x3 and not x2 and not x1);*
!x2!x1 !x2x1 x2x1 x2!x1
00 01 11 10
00 1
!x4!x3
01 1
!x4x3
11 1 1
x4x3
10 1 1
x4!x3
y <= (x3 and x1) or
(not x4 and x3 and x2 and x1) or
(not x3 and x3 x2 and not x1);
x3 or (x2 and x1)
(x3 or x1) and (x2 or x3)
y := x2 or x3
(x3 or x1) and y
(x3 and y) or (x1 and y)
(x3 and (x2 or x3)) or (x1 and (x2 or x3))
(x3 and x2) or (x3 and x3) or (x1 and x2) or (x1 and x3)
(x3 and x2) or 1 or (x1 and x2) or (x1 and x3)
(x3 and x2) or (x3 and x1) or (x1 and x2)
