how to add two binary numbers manually code example

Example: program to add two binary numbers

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