Utility functions to facilitate computations



In [48]:

    
def nand(a, b):
    return not a & b



In [49]:

    
def _and(a, b):
    return a & b



In [50]:

    
def _or(a, b):
    return a | b



In [51]:

    
def nor(a, b):
    return not a | b

Problem 3



In [52]:

    
inputs = [(0, 0, 0),
          (0, 0, 1),
          (0, 1, 0), 
          (0, 1, 1),
          (1, 0, 0),
          (1, 0, 1),
          (1, 1, 0),
          (1, 1, 1)]



In [53]:

    
for a, b, c in inputs:
    print((a & b) | (b & c) | (a & c))

Problem 4



In [54]:

    
inputs = [(0, 0),
          (1, 0),
          (0, 1),
          (1, 1)]



In [55]:

    
for a, b in inputs:
    print( not ((a & b) | ((not a) & (not b))) )









    



False
True
True
False

Problem 5



In [56]:

    
def circuit(s, i3, i2, i1, i0):
    o3 = _and(not s, i2)
    o2 = _or(_and(s, i3), _and(not s, i1))
    o1 = _or(_and(i2, s), _and(not s, i0))
    o0 = _and(i1, s)
    
    return o3, o2, o1, o0



In [57]:

    
circuit(1, 1, 0, 1, 1)









    Out[57]:





(0, 1, 0, 1)

Problem 6



In [58]:

    
inputs = [(0, 0),
          (1, 0),
          (0, 1),
          (1, 1)]



In [59]:

    
for a, b in inputs:
    print(nand(nand(a, nand(a, b)), nand(b, nand(a, b))))









    



False
True
True
False

Problem 7



In [38]:

    
def circuit(a, b):
    return _or(_and(not a, b), _and(not b, a))



In [39]:

    
for a, b in inputs:
    for c in [0, 1]:
        print(circuit(circuit(a, b), c))

Problem 8



In [45]:

    
inputs = [(0, 0, 0),
          (0, 0, 1),
          (0, 1, 0), 
          (0, 1, 1),
          (1, 0, 0),
          (1, 0, 1),
          (1, 1, 0),
          (1, 1, 1)]



In [47]:

    
for a, b, c in inputs:
    print(_or(_and(not b, not c), _and(b, c)))