public class AddBinary {

public String addBinary(String a, String b) {

StringBuilder sb = new StringBuilder();

for (int i = a.length() - 1, j = b.length() - 1, flag = 0; i >= 0 || j >= 0 || flag > 0; i--, j--) {

int k1 = i >= 0 ? a.charAt(i) - '0' : 0;

int k2 = j >= 0 ? b.charAt(j) - '0' : 0;

int sum = k1 + k2 + flag;

sb.append(sum % 2);

flag = sum / 2;

}

return sb.reverse().toString();

}

}