#this one solution is a bit cheating cause def sum_bin(bin_a, bin_b): return bin(int(bin_a, 2) + int(bin_b, 2))[2:] def sum_bin2(bin_a, bin_b): # we assume equal length numbers remainder = 0 sum = '' for i in range(len(bin_a) - 1, -1, -1): # iterate from last character to zero res = int(bin_a[i]) + int(bin_b[i]) + remainder remainder = res // 2 digit = res % 2 sum = str(digit) + sum return '1' + sum if remainder else sum