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

using namespace std;

string FloatToAny(double number, int b);
double AnyToFloat(string number, int b);

int main() {

     for(int i = 2; i < 10; ++i) {
         double num = 1/ static_cast<float>(i);
         for(int base = 2; base < 16; ++base) {
             string binaryRep = FloatToAny(num,base);

             cout << num << " = "
                  << binaryRep << "_" << base << " =  "
                  << AnyToFloat(binaryRep,base) << endl;
         }
         cout << endl;
     }

     return 0;
}

int CharToDigit(char c) {
   if (c >= '0' and c <= '9') {
      return c-'0';
   } else {
      return 10 + toupper(c)-'A';
   }
}

char DigitToChar(int d) {
    if (d <= 9) {
       return d + '0';
    } else {
       return (d-10)+'A';
    }
}


double AnyToFloat(string number, int b) {
    double num{0};
    double power {1/static_cast<double>(b)};

    for(size_t i = 1; i < number.length(); ++i) {
       int digit = CharToDigit(number[i]);
       num += digit * power;
       power /= static_cast<double>(b);
    }

    return num;
}


string FloatToAny(double number, int b){

    int digit{0};
    string numberString{"."};
    int limit = 0;

    while (number > 0 and limit < 10) {
      
       number *= b; 
       digit = int(number);
       number = number - digit;

       numberString += DigitToChar(digit);
       limit ++;
    }

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

    return numberString;
}