# The Bit class.
class Bit:
    '''A single bit class.
    All of the operations: "invert/not", "or", "and" and "full_adder" are built directly or indirectly on "nor".
    '''

    def __init__(self, a_val):
        '''Instantiate the Bit object with any valid inputs'''
        if a_val not in [0, 1, 4, 5]:
            raise ValueError
        self.val = a_val

    def nor(self, b):
        ''' Return a NOR b.
        Yes I could have written this in one line but this version doesn't use any binary logical operators.
        '''
        if self:
            return ZERO
        elif b:
            return ZERO
        else:
            return ONE

    def __str__(self):
        return str(self.val)

    def __bool__(self):
        ''' True if it is 4 or 5; False if it is 0 or 1. '''
        if self.val > 3:
            return True
        elif self.val < 2:
            return False

    def __invert__(self):
        ''' Return the NOT of self. Built on NOR.
        '''
        return self.nor(self)


    def __or__(self, b):
        ''' Return self OR b.
        Built on NOR and NOT. '''
        return ~self.nor(b)


    def __and__(self, b):
        ''' Return self AND b.
        Built on NOT and OR using DeMorgan's law. '''
        return ~(~self | ~b)


    def full_adder(self, b):
        ''' Return self + b + carry as a single bit with carry set as well. Built on AND, OR and NOT.
        See Figure 3.15 in the textbook.
        '''
        global carry  # it is processor global status
        bitsum = (((self|b)&~(self&b))|carry)&~(((self|b)&~(self&b))&carry)
        carry = (self & b) | (self & carry) | (b & carry)
        return carry


ZERO = Bit(0)  # or Bit(1)
ONE  = Bit(4)
carry = ZERO
c = Bit(4)
d = Bit(5)
e = Bit(5)
f = Bit(5)

print(c.full_adder(d))
print(carry)
print(e.full_adder(f))
print(carry)