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'))