Add Binary

public class Solution {
    public String addBinary(String a, String b) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(a == null || b == null)
            return null;
        String result = "";
        if(a.isEmpty() || b.isEmpty())
            return result;
        return helpler(result, a, b);
    }
    private String helpler(String result, String a, String b)
    {
        int carrier = 0;
        int m = a.length()-1;
        int n = b.length()-1;
        for(int i=0; i<=Math.max(m, n); i++)
        {
            int c_a = (m>=i) ? a.charAt(m-i)-'0' : 0;
            int c_b = (n>=i) ? b.charAt(n-i)-'0' : 0;
            result = (c_a+c_b+carrier)%2 + result;
            carrier = (c_a+c_b+carrier)/2;
        }
        if(carrier == 0)
            return result;
        else{
            result = "1"+result;
            return result;
        }
    }
}