[Leetcode] Add Binary

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

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

    string addBinary(string a, string b) {
        string ret;
        int i = a.size() - 1;
        int j = b.size() - 1;
        int carry = 0;
        while(i >= 0 || j >= 0 || carry > 0)
        {
            int da = i < a.size() ? a[i] - '0' : 0;
            int db = j < b.size() ? b[j] - '0': 0;
            //the value
            int d = (da + db + carry) % 2;
            //the carry
            carry = (da + db + carry) / 2;
            ret.insert(ret.begin(),1, d + '0');
            i--;
            j--;
        }
        
        return ret;
    }