Add Binary

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

For example,

a = "11"

b = "1"

Return "100".

normalize two string to be the same length, then add each char.

public String addBinary(String a, String b) {
        if (a==null||b==null||a.isEmpty()||b.isEmpty()) {
            return "";
        }

        if (a.length()<b.length()) {
            return addBinary(b,a);
        }

        int diff = a.length()-b.length();

        for (int i=diff; i>0; i--) {
            b = '0' + b;
        }

        int index = a.length()-1;
        StringBuilder sb = new StringBuilder();
        int carryOn = 0;
        while (index>=0) {
            int sum = (a.charAt(index)-'0') + (b.charAt(index)-'0') + carryOn;
            if (sum>=2) {
                carryOn = 1;
            } else {
                carryOn = 0;
            }
            sb.insert(0, sum%2);
            index = index-1;
        }

        if (carryOn>0) {
            sb.insert(0,'1');
        }

        return sb.toString();
    }