def add_binary_nums(x,y):
max_len = max(len(x), len(y))
x = x.zfill(max_len)
y = y.zfill(max_len)
result = ''
carry = 0
for i in range(max_len-1, -1, -1):
r = carry
r += 1 if x[i] == '1' else 0
r += 1 if y[i] == '1' else 0
result = ('1' if r % 2 == 1 else '0') + result
carry = 0 if r < 2 else 1
if carry !=0 : result = '1' + result
return result.zfill(max_len)
print(add_binary_nums('11', '1'))
print(add_binary_nums('10', '10'))
print(add_binary_nums('111', '111'))
print(add_binary_nums('1111111', '1'))
