C++ Sets and Subsets

I am trying to find the subsets and output them with binary representation.

EXAMPLE:

000:EMPTY 001:C 010:B 011:B C 100:A 101:A C 110:A B 111:A B C

I have the following code that finds all subsets but not sure about the binary??

#include <iostream>
using namespace std;

    enter code here

void recsub(string sofar, string rest){
  if(rest=="") cout<<sofar<<endl;
  else{
    recsub(sofar+rest[0], rest.substr(1)); //including first letter
    recsub(sofar, rest.substr(1)); //recursion without including first letter.
  }
}
void listsub(string str){
  recsub("",str);
}
int main(){
  listsub("abc");
  return 0;
}