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

For example,
a = "11"
b = "1"

Return "100".

具体一位一位地加就行了，考虑进位的问题。还有最后记得把生成的string反过来再返回，因为我们是从最低位开始加的。

public class Solution {
    public String addBinary(String a, String b) {
        if(a == null || a.length() == 0)
            return b;
        if(b == null || b.length() == 0)
            return a;
        
        StringBuilder res = new StringBuilder();
        
        int i = a.length() - 1;
        int j = b.length() - 1;
        int digit;
        int carry = 0;
        
        while(i >= 0 && j >= 0){
            digit = (int)(a.charAt(i) - '0' + b.charAt(j) - '0' + carry);
            carry = digit / 2;
            digit %= 2;
            
            res.append(digit);
            i--;
            j--;
        }
        
        while(i >= 0){
            digit = (int)(a.charAt(i) - '0' + carry);
            carry = digit / 2;
            digit %= 2;
            
            res.append(digit);
            i--;
        }
        
        while(j >= 0){
            digit = (int)(b.charAt(j) - '0' + carry);
            carry = digit / 2;
            digit %= 2;
            
            res.append(digit);
            j--;
        }
        //don't forget to add the final carry(if exists)
        if(carry > 0){
            res.append(carry);
        }
        
        return res.reverse().toString();
    }
}