#include <iostream>
#include <string>
#include <cmath>

using namespace std;

string FloatToBinary(double num);
double BinaryToFloat(string binary) ;

int main() {

     for(int i = 2; i < 10; ++i) {
         double num = 1/ static_cast<float>(i);
         string binaryRep = FloatToBinary(num);

         cout << num << " = "
              << binaryRep << "_2 =  "
              << BinaryToFloat(binaryRep) << endl;
     }

     return 0;
}

double BinaryToFloat(string binary) {
    double num{0};
    double pow {1/2.0};

    for(size_t i = 1; i < binary.length(); ++i) {
       if (binary[i] == '1') {
           num += pow;
       }
       pow /= 2.0;
    }

    return num;
}


string FloatToBinary(double num){

    char digit;
    string binaryString{"."};

    while (num > 0) {

       num *= 2.0;
       if (num >= 1.0) {
          digit = '1';
          num -=1.0;
       } else {
          digit = '0';
       }

       binaryString += digit;
    }

    if (binaryString.length() == 1) {
       binaryString = "0";
    }

    return binaryString;
}