New and improved binary class

Right... here it is - flames and comments all welcome:

#ifndef __BINARY__
#define __BINARY__

#include <iostream>
#include <string>
#include <limits>
#include <exception>

class binary
{
public:
    class bad_size : public std::exception
    {
        virtual const char* what() const throw()
        {
            return "Number of Bits != Number of digits!";
        }
    } bad_size;

    class bad_range : public std::exception
    {
        virtual const char* what() const throw()
        {
            return "Out of Range";
        }
    } bad_range;

    template <typename T>
    binary(const T& n)
    {
        const unsigned int bits =
std::numeric_limits<T>::digits; for (unsigned int i = 0; i < bits; i++)
            digits.insert(digits.begin(), (n & (1 << i)) ?
'1' : '0');

        // digits.insert(digits.begin(), 'E'); // tests
exception if (digits.size() != bits)
            throw bad_size;
    }

    const bool test(const unsigned int n) const
    {
        if (n > digits.size() || n == 0)
            throw bad_range;

        return (digits[n - 1] == '1') ? true : false;
    }

    void set(const unsigned int n)
    {
        if (n > digits.size() || n == 0)
            throw bad_range;

        digits[n - 1] = '1';
    }

    friend std::ostream& operator<<(std::ostream& stream, const
binary& bin) {
        return stream << bin.digits;
    }

private:
    std::string digits;
};

#endif // __BINARY__

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