add two binary number

#include<bits/stdc++.h>
#include<iostream>
using namespace std;
        int main(){
        string a;string b;string result;
        cin>>a>>b;
         int i=a.size();int j=b.size();int carry=0;
        while(i>0||j>0||carry==1){
           if(i>0) carry+=a[--i]-'0';
           if(j>0 ) carry+=b[--j]-'0';
            result+=char(carry%2+'0');
            carry=carry/2;
        }
        reverse(result.begin(),result.end());
        cout<<result<<endl;
        return 0;




    }