#!/usr/bin/env python
# coding: utf-8

# # Logik
# 
# * `and`: und
# * `or`: oder
# * `not`: negation
# * `^`: xor
# 
# Wahr, Falsch oder [Unbekannt](http://de.wikipedia.org/wiki/Unvollständigkeitssatz).

# In[1]:


True and True


# In[2]:


not True or not False


# In[3]:


not (True or False)


# In[4]:


True ^ False


# In[5]:


True ^ True


# In[6]:


not (False or False)


# ## Wahrheitstabelle

# In[7]:


fmt = lambda t : "X" if t else "."


# In[8]:


def print_table(prop):
    from itertools import product

    print("A  B  C  =>  P")
    print("-" * 14)

    for state in product([True, False], repeat=3):
        args = '  '.join(fmt(s) for s in state)
        res = prop(*state)
        print("{}  =>  {}".format(args, fmt(res)))


# In[9]:


prop1 = lambda a, b, c : (a or (not a and b)) and c
print_table(prop1)


# In[10]:


prop2 = lambda a, b, c : (a or b) and c
print_table(prop2)


# In[11]:


prop3 = lambda a, b, c : a and (b ^ c)
print_table(prop3)


# ## Addition zweier Boolscher Vektoren
# 
# Die zwei Vektoren werden nach den üblichen Regeln addiert.

# In[12]:


a = [True, True, False, True, True,  False]
b =             [True,  True, False, False]


# In[13]:


def boolean_add(a, b):
    size = max(len(a), len(b))
    # padding
    for v in [a, b]:
        while len(v) < size:
            v.insert(0, False)
            
    result = []
    c = False
    for pos in reversed(range(size)):
        s = a[pos] ^ b[pos] ^ c
        c = (a[pos] and b[pos]) or (c and (a[pos] ^ b[pos]))
        result.insert(0, s)
    result.insert(0, c)
    return result


# In[14]:


ab = boolean_add(a, b)
ab


# In[15]:


def boolean_to_decimal(b):
    result = 0
    for i, x in enumerate(reversed(b)):
        result += 2**i * x
    return result


# In[16]:


print boolean_to_decimal(a)
print boolean_to_decimal(b)
print boolean_to_decimal(ab)