Here is my Java Solution:

```
class Solution {
public String addBinary(String a, String b) {
StringBuffer res = new StringBuffer();
int N = a.length(), M = b.length();
int i = N - 1, j = M - 1;
int carry = 0;
while (i>=0 || j>=0) {
int sum = carry;
if (i >= 0) sum += a.charAt(i--) - '0';
if (j >= 0) sum += b.charAt(j--) - '0';
carry = sum / 2;
res.insert(0,String.valueOf(sum % 2));
}
if (carry == 1) res.insert(0,'1');
return res.toString();
}
}
```