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Digitales Multimeter Anordnung der Segmente a bis g Angenommen, eine 7-Segment-Anzeige besitzt vier digitale Eingänge zur Ansteuerung. Dann ergibt sich folgende Belegung der Eingänge (x3, x2, x1, x0) für die sieben Segmente (a, b, c, d, e, f, g):
Alle 128 möglichen Kombinationen einer Siebensegmentanzeige.
Eingänge und Segmente
x3
x2
x1
x0
Zeichen
a
b
c
d
e
f
g
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
1
0
0
1
1
3
1
1
1
1
0
0
1
0
1
0
0
4
0
1
1
0
0
1
1
0
1
0
1
5
1
0
1
1
0
1
1
0
1
1
0
6
1
0
1
1
1
1
1
0
1
1
1
7
1
1
1
0
0
0
0
1
0
0
0
8
1
1
1
1
1
1
1
1
0
0
1
9
1
1
1
1
0
1
1
1
0
1
0
A
1
1
1
0
1
1
1
1
0
1
1
B
0
0
1
1
1
1
1
1
1
0
0
C
1
0
0
1
1
1
0
1
1
0
1
D
0
1
1
1
1
0
1
1
1
1
0
E
1
0
0
1
1
1
1
1
1
1
1
F
1
0
0
0
1
1
1
Schaltfunktionen für die Segmente
Bearbeiten
Folgende Schaltfunktionen in Disjunktiver Minimalform (DMF) ergeben sich aus obiger Logiktabelle:
a)
x
3
x
2
¯
x
1
¯
+
x
3
¯
x
2
x
0
+
x
2
¯
x
0
¯
+
x
3
x
0
¯
+
x
1
x
0
¯
+
x
3
¯
x
1
+
x
2
x
1
{\displaystyle x_{3}{\bar {x_{2}}}{\bar {x_{1}}}+{\bar {x_{3}}}x_{2}x_{0}+{\bar {x_{2}}}{\bar {x_{0}}}+x_{3}{\bar {x_{0}}}+x_{1}{\bar {x_{0}}}+{\bar {x_{3}}}x_{1}+x_{2}x_{1}}
b)
x
3
¯
x
1
¯
x
0
¯
+
x
3
x
1
¯
x
0
+
x
3
¯
x
1
x
0
+
x
2
¯
x
0
¯
+
x
3
¯
x
2
¯
{\displaystyle {\bar {x_{3}}}{\bar {x_{1}}}{\bar {x_{0}}}+x_{3}{\bar {x_{1}}}x_{0}+{\bar {x_{3}}}x_{1}x_{0}+{\bar {x_{2}}}{\bar {x_{0}}}+{\bar {x_{3}}}{\bar {x_{2}}}}
c)
x
2
¯
x
1
¯
+
x
3
¯
x
1
¯
+
x
3
x
2
¯
+
x
3
¯
x
2
+
x
1
¯
x
0
+
x
3
¯
x
0
+
x
2
¯
x
0
{\displaystyle {\bar {x_{2}}}{\bar {x_{1}}}+{\bar {x_{3}}}{\bar {x_{1}}}+x_{3}{\bar {x_{2}}}+{\bar {x_{3}}}x_{2}+{\bar {x_{1}}}x_{0}+{\bar {x_{3}}}x_{0}+{\bar {x_{2}}}x_{0}}
d)
x
2
x
1
¯
x
0
+
x
3
x
1
¯
x
0
+
x
2
¯
x
0
¯
+
x
3
x
2
¯
+
x
1
x
0
¯
+
x
1
x
2
¯
{\displaystyle x_{2}{\bar {x_{1}}}x_{0}+x_{3}{\bar {x_{1}}}x_{0}+{\bar {x_{2}}}{\bar {x_{0}}}+x_{3}{\bar {x_{2}}}+x_{1}{\bar {x_{0}}}+x_{1}{\bar {x_{2}}}}
e)
x
1
x
0
¯
+
x
3
x
1
+
x
3
x
2
+
x
2
¯
x
0
¯
{\displaystyle x_{1}{\bar {x_{0}}}+x_{3}x_{1}+x_{3}x_{2}+{\bar {x_{2}}}{\bar {x_{0}}}}
f)
x
3
¯
x
2
x
1
¯
+
x
1
¯
x
0
¯
+
x
3
x
0
¯
+
x
3
x
2
¯
+
x
2
x
0
¯
+
x
3
x
1
{\displaystyle {\bar {x_{3}}}x_{2}{\bar {x_{1}}}+{\bar {x_{1}}}{\bar {x_{0}}}+x_{3}{\bar {x_{0}}}+x_{3}{\bar {x_{2}}}+x_{2}{\bar {x_{0}}}+x_{3}x_{1}}
g)
x
3
¯
x
2
x
0
¯
+
x
3
¯
x
2
x
1
¯
+
x
2
x
1
¯
x
0
+
x
3
x
2
¯
+
x
1
x
0
¯
+
x
2
¯
x
1
+
x
3
x
1
+
x
3
x
0
{\displaystyle {\bar {x_{3}}}x_{2}{\bar {x_{0}}}+{\bar {x_{3}}}x_{2}{\bar {x_{1}}}+x_{2}{\bar {x_{1}}}x_{0}+x_{3}{\bar {x_{2}}}+x_{1}{\bar {x_{0}}}+{\bar {x_{2}}}x_{1}+x_{3}x_{1}+x_{3}x_{0}}
Beschränkt man sich auf die Dezimalziffern, so vereinfachen sich die Funktionen zu:
a)
x
3
¯
x
1
+
x
2
x
0
+
x
3
+
x
2
¯
x
0
¯
{\displaystyle {\bar {x_{3}}}x_{1}+x_{2}x_{0}+x_{3}+{\bar {x_{2}}}{\bar {x_{0}}}}
b)
x
2
¯
+
x
0
¯
x
1
¯
+
x
1
x
0
{\displaystyle {\bar {x_{2}}}+{\bar {x_{0}}}{\bar {x_{1}}}+x_{1}x_{0}}
c)
x
0
+
x
1
¯
+
x
2
{\displaystyle x_{0}+{\bar {x_{1}}}+x_{2}}
d)
x
3
+
x
2
¯
x
1
+
x
1
x
0
¯
+
x
2
x
1
¯
x
0
+
x
2
¯
x
0
¯
{\displaystyle x_{3}+{\bar {x_{2}}}x_{1}+x_{1}{\bar {x_{0}}}+x_{2}{\bar {x_{1}}}x_{0}+{\bar {x_{2}}}{\bar {x_{0}}}}
e)
x
2
¯
x
0
¯
+
x
1
x
0
¯
{\displaystyle {\bar {x_{2}}}{\bar {x_{0}}}+x_{1}{\bar {x_{0}}}}
f)
x
3
+
x
2
x
1
¯
+
x
1
¯
x
0
¯
+
x
2
x
0
¯
{\displaystyle x_{3}+x_{2}{\bar {x_{1}}}+{\bar {x_{1}}}{\bar {x_{0}}}+x_{2}{\bar {x_{0}}}}
g)
x
3
+
x
2
x
1
¯
+
x
3
¯
x
2
¯
x
1
+
x
1
x
0
¯
{\displaystyle x_{3}+x_{2}{\bar {x_{1}}}+{\bar {x_{3}}}{\bar {x_{2}}}x_{1}+x_{1}{\bar {x_{0}}}}
