Add Binary

public class Solution {
    public String addBinary(String a, String b) {
        if (a == null || b == null) {
    		throw new IllegalArgumentException("");
    	}
    	int i = a.length() - 1, j = b.length() - 1, carry = 0;
    	StringBuilder sb = new StringBuilder();
    	while (i >=0 || j >= 0 || carry != 0) {
    		int numA = 0;
    		if (i >= 0) 
    			numA = a.charAt(i) - '0';
    		int numB = 0;
    		if (j >= 0) 
    			numB = b.charAt(j) - '0';
    		int sum = (numA + numB + carry) % 2;
    		carry = (numA + numB + carry) / 2;
    		sb.insert(0, sum);
    		i--;
    		j--;
    	}
    	return sb.toString();
    }
}