Uebungsblatt 5

Name: Joe User
Tutor: ????
Email: juser@icp.uni-stuttgart.de

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AUFGABE 5.1 (Boole'sche Algebra)
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5.1.1
Wertetafel

a | b | F
---------
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0

==========
5.1.2

Gesetze:
1. Assoziativität
  a or (b or c) = (a or b) or c
  a and (b and c) = (a and b) and c

2. Distributivität
  a or (b and c) = (a or b) and (a or c)
  a and (b or c) = (a and b) or (a and c)

3. Kommutativität
  a and b = b and a
  a or b = b or a

4. Absorption
  a or (a and b) = a
  a and (a or b) = a

5. Komplement
  a or not a = True
  a and not a = False

6. Neutralität
  a or False = a
  a and True = a

7. Idempotenz
  a and a = a
  a or a = a

8. Extremalgesetz
  a or True = True
  a and False = False

9. Doppelnegation
  not (not a) = a

10. Dualität
  not True = False
  not False = True

11. De Morgan
  not (a or b) = not a and not b
  not (a and b) = not a or not b


F     = not (not (not (a and b) and a) and not (not (a and b) and b))
#11*2 = not (not ((not a or not b) and a) and not((not a or not b) and b))
#2*2  = not (not ((not a and a) or (not b and a)) 
               and not ((not a and b) or (not b and b)))
#5*2  = not (not (False or (not b and a)) and not ((not a and b) or False)
#6*2  = not (not (not b and a) and not (not a and b))
#11*2 = not ((b or not a) and (a or not b))
#11   = not (b or not a) or not (a or not b)
#11*2 = (not b and a) or (not a and b)
      = (a and not b) or (not a and b)
      = a xor b

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5.1.3
Zeige:
a or False = a :

      a or False
#5r = a or (a and not a)
#4  = a


a or a = a:

      a or a
#5r = a or (a and True)
#4  = a

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AUFGABE 5.2 (Zahlensysteme)
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5.2.1
a = 4*7^0 + 3*7^1 + 2*7^2 + 1*7^3 = 4 + 21 + 98 + 343 = 466
b = 1D2
c = 4D2
d = 2322
e = 3412
f = 11001101
g = 10111
h = 201
i = 245
j = 81
k = A5

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5.2.2.1
Welchen Vorteil hat das Hexadezimalsystem gegenueber dem Dezimalsystem
im Computerumfeld?

Es ist einfacher, Zahlen zwischen dem Hexadezimalsystem und dem vom
Computer verwendete Binärsystem hin- und herzurechnen.

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5.2.2.2
Welchen Vorteil hat das Hexadezimalsystem gegenueber dem Oktalsystem
im Computerumfeld?

Eine Stelle im Hexadezimalsystem entspricht 4 binären Stellen, im
Oktalsystem 3 binären Stellen. Der Computer rechnet normalerweise in
Bytes (8 bit), so daß ein Byte genau zwei Hexadezimalstellen
entspricht.

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AUFGABE 5.3 (nohtyP)
==========
Skript:
n = 123456

print "n = ", n

nr = 0
while n > 0:
    ziffer = n % 10
    n = n / 10
    nr = nr * 10 + ziffer

print "nr = ", nr