Add binary

Given two binary strings, return their sum (also a binary string).
Example
a = 11
b = 1
Return 100

二进制加法，解题思路就是从尾到头遍历，一个个数提出来相加，还需要一个adder来存储当前是否加一的状态。如果a或b字符串还没有遍历完，继续执行上面的步骤，最后还需要检测一下adder是否为1。

public class Solution {
    /**
     * @param a a number
     * @param b a number
     * @return the result
     */
    public String addBinary(String a, String b) {
        // Write your code here
        if(a == null || b == null){
            return a+b;
        }
        
        int m = a.length()-1;
        int n = b.length()-1;
        int adder = 0;
        String rst = "";
        
        while( m >= 0 && n >= 0) {
            int sum = (int)(a.charAt(m) - '0') + (int)(b.charAt(n) - '0') + adder;
            rst = String.valueOf(sum % 2) + rst;
            adder = sum/2;
            m--;
            n--;
        }
        
        while(m >= 0) {
            int sum = (int)(a.charAt(m) - '0') + adder;
            rst = String.valueOf(sum % 2) + rst;
            adder = sum/2;
            m--;
        }
        
        while(n >= 0) {
            int sum = (int)(b.charAt(n) - '0') + adder;
            rst = String.valueOf(sum % 2) + rst;
            adder = sum/2;
            n--;
        }
        
        if(adder == 1) {
            rst = "1" + rst;
        }
        
        return rst;
    }
}