What is the best way to convert unsigned integers to their octal representations and vice versa in C++?

Currently I'm using while loops:

std::string to_octal(unsigned int num)
{
    int place = 1, remainder, octal = 0;
    while (num != 0)
    {
        remainder = num % 8;
        decimal /= 8;
        octal += remainder * place;
        place *= 10;
    }
    return std::to_string(octal);
}

unsigned int to_num(std::string octal)
{
    unsigned int octal_n = std::stoi(octal);
    int place = 1, remainder, num = 0;
    while (num != 0)
    {
        remainder = octal_n % 10;
        octal_n /= 10;
        num += remainder * place;
        place *= 8;
    }
    return num;
}

Which seems inefficient. Is there a better way to do this?

There is no such thing as decimal unsigned int, hexadecimal unsigned int or octal unsigned int. There is only one unsigned int. There is a difference only when you want to print an object of that type to the terminal or a file. From that point of view, the function

unsigned int decimal_to_octal(unsigned int decimal);

does not make sense at all. It makes sense to use:

struct decimal_tag {};
struct hexadecimal_tag {};
struct octal_tag {};

// Return a string that represents the number in decimal form
std::string to_string(unsigned int number, decimal_tag);

// Return a string that represents the number in hexadecimal form
std::string to_string(unsigned int number, hexadecimal_tag);

// Return a string that represents the number in octal form
std::string to_string(unsigned int number, octal_tag);

and their counterparts.

// Extract an unsigned number from the string that has decimal representation
unsigned int to_number(std::string const& s, decimal_tag);

// Extract an unsigned number from the string that has hexadecimal representation
unsigned int to_number(std::string const& s, hexadecimal_tag);

// Extract an unsigned number from the string that has octal representation
unsigned int to_number(std::string const& s, octal_tag);

---

Here's demonstrative program:

#include <iostream>
#include <string>
#include <iomanip>
#include <sstream>

struct decimal_tag {};
struct hexadecimal_tag {};
struct octal_tag {};

// Return a string that represents the number in decimal form
std::string to_string(unsigned int number, decimal_tag)
{
   std::ostringstream str;
   str << std::dec << number;
   return str.str();
}

// Return a string that represents the number in hexadecimal form
std::string to_string(unsigned int number, hexadecimal_tag)
{
   std::ostringstream str;
   str << std::hex << number;
   return str.str();
}

// Return a string that represents the number in octal form
std::string to_string(unsigned int number, octal_tag)
{
   std::ostringstream str;
   str << std::oct << number;
   return str.str();
}

// Extract an unsigned number from the string that has decimal representation
unsigned int to_number(std::string const& s, decimal_tag)
{
   std::istringstream str(s);
   unsigned int number;
   str >> std::dec >> number;
   return number;
}

// Extract an unsigned number from the string that has hexadecimal representation
unsigned int to_number(std::string const& s, hexadecimal_tag)
{
   std::istringstream str(s);
   unsigned int number;
   str >> std::hex >> number;
   return number;
}

// Extract an unsigned number from the string that has octal representation
unsigned int to_number(std::string const& s, octal_tag)
{
   std::istringstream str(s);
   unsigned int number;
   str >> std::oct >> number;
   return number;
}

int main()
{
   unsigned int n = 200;
   std::cout << "200 in decimal: " << to_string(n, decimal_tag()) << std::endl;
   std::cout << "200 in hexadecimal: " << to_string(n, hexadecimal_tag()) << std::endl;
   std::cout << "200 in octal: " << to_string(n, octal_tag()) << std::endl;

   std::cout << "Number from decimal form (200): " << to_number("200", decimal_tag()) << std::endl;
   std::cout << "Number from hexadcimal form (c8): " << to_number("c8", hexadecimal_tag()) << std::endl;
   std::cout << "Number from octal form (310): " << to_number("310", octal_tag()) << std::endl;
}

and its output:

200 in decimal: 200
200 in hexadecimal: c8
200 in octal: 310
Number from decimal form (200): 200
Number from hexadcimal form (c8): 200
Number from octal form (310): 200