Leetcode - Add Binary

Given two binary strings, return their sum (also a binary string).

For example,
a = "11"
b = "1"
Return "100".

 

    public String addBinary(String a, String b) {
        if (a == null && b == null) return null;
        if (a == null || a.length() == 0) return b;
        if (b == null || b.length() == 0) return a;
        
        if (a.length() > b.length())
            return addBinary(b, a);
        int i = a.length() - 1;
        int j = b.length() - 1;
        StringBuilder sum = new StringBuilder();
        int carry = 0, curr = 0;
        while (i >= 0 && j >= 0) {
            curr = a.charAt(i--) - '0' + b.charAt(j--) - '0' + carry;
            carry = curr >> 1;
            sum.append(curr >= 2 ? curr - 2 : curr);
        }
        while (j >= 0) {
            curr = b.charAt(j--) - '0' + carry;
            carry = curr >> 1;
            sum.append(curr >= 2 ? curr - 2 : curr);
        }
        if (carry > 0)
            sum.append(carry);
        return sum.reverse().toString();
    }