Leetcode 67. Add Binary

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

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

 

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;
        
        var sb = new StringBuilder();
        int shift = 0;
        
        int i = a.Length - 1, j = b.Length - 1;
        while (i >= 0 || j >= 0)
        {
            if (i >= 0)
            {
                shift += ((int)a[i] - (int)'0');
                i--;
            }
            
            if (j >= 0)
            {
                shift += ((int)b[j] - (int)'0');
                j--;
            }
            
            sb.Insert(0, shift % 2);
            shift /= 2;
        }
        
        if (shift != 0) sb.Insert(0, shift % 2);
        
        return sb.ToString();
    }
}