Add Binary

class Solution {
public:
    string addBinary(string a, string b) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        string retString;
        if( a.empty() )
            return b;
        else if( b.empty() )
            return a;
        int length = a.length() > b.length() ? a.length() : b.length();
        int carry = 0 ;
        for( int indx = 0 ; indx < length ; ++indx )
        {
            if( indx < a.length() && indx < b.length() )
            {
                int num = a[a.size() - indx -1 ] - '0' + b[b.size() - indx - 1 ] - '0' + carry;
                carry = num/2;
                
                retString.push_back('0'+num%2);
            }
            else if( indx < a.length() && indx >= b.length() )
            {
                int num = a[a.size() - indx - 1] - '0' + carry;
                carry = num/2;
                retString.push_back('0'+num%2);
            }
            else if( indx < b.length() && indx >= a.length() )
            {
                int num = b[b.size() - indx - 1] - '0' + carry;
                carry = num/2;
                retString.push_back('0'+num%2);
            }
        }
        if( carry ) 
              retString.push_back('1');
        reverse(retString.begin() , retString.end() );
        if( retString.empty() )
            retString.push_back('0');
        return retString;
        
    }
};