def chunks(l, n):
    # 12345 -> [1,2,3,4,5] with .list() method
    l = str(l)
    for i in xrange(0, len(l), n):
        yield int(l[i:i+n])

def merge(list):
    # [1,2,3] -> 123
    s = ''
    for elem in list:
        s+=str(elem)
    return int(s)

class Binary:
    def __init__(self, value):
        self.value = value
    def add(self, add_value):
        s1 = list(chunks(add_value,1))
        s2 = list(chunks(self.value,1))

        if len(s1) < len(s2):
            for i in xrange(0, len(s2)-len(s1)):
                s1.insert(0,0)
        elif len(s1) > len(s2):
            for i in xrange(0, len(s1)-len(s2)):
                s2.insert(0,0)
        s3 = []
        for i in xrange(len(s1)-1, -1, -1):
            if s1[i]+s2[i] == 2:
                s3.insert(0,0)
                s3.insert(0,1)
            else:
                s3.insert(0, s1[i]+(s2[i]))
        self.value = merge(s3)
        return self
    def view(self):
        print self.value
        return self

bin = Binary(1).add(110).view()
bin.add(1).view()

def bin_sum(s1,s2):
    if len(s1) > len(s2):
        while len(s1)>len(s2):
            s2 = '0' +s2
    else:
        while len(s1)<len(s2):
            s1= '0' +s1
    s= ''
    shift = '0'
    for i in xrange(len(s1)-1,-1,-1):
        d = int(s1[i])+int(s2[i])+int(shift)
        shift = d / 2
        d = d % 2
        s = (str(d) + s)

    if shift != 0:
        s = '1' + s
    return s

s1 = '111'
s2 = '111'
print bin_sum(s1,s2)

s1 = '10101010'
s2 = '1001'

s1, s2 = max(s1, s2), min(s1, s2)
s2 = '0' * (len(s1) - len(s2)) + s2
s = ''
d = 0

for i in range(len(s1) - 1, -1, -1):
    d = int(s1[i]) + int(s2[i]) + d
    s = str(d % 2) + s
    d = d / 2

print(str(d) + s)