/*  File binrep1.cpp   
    Version 1 (simplified)
    J. Shinnerl, 10/18/99; 1/29/02.

    This program prints out the binary digits of an integer
    entered by the user at run time.  Because the digits are
    acquired by integer division using %,  they are obtained and
    stored in reverse order in an array.  To display them in the
    usual order, the digits are reversed again during printing: 
    the last digit stored in the array is the first digit printed,
    and the first digit stored in the array is the last digit printed.

    To determine the size of the array needed to hold the binary
    digits of any integer, we take the log2 (log base 2) of INT_MAX.
    INT_MAX is an integer constant defined in <climits> specifying 
    the largest integer representable on the given operating platform.
    Because the <cmath> library only contains log (log base-e) and log10
    (log base-10), we use the base-changing formula 

                 log2(x) = log10(x)/log10(2)

    to express log2 in terms of log10.   Deriving the base-changing
    formula is an easy exercise:

          y  ==  log2(x)   <==>  x  == 2^y  <==> log10(x) == log10(2^y)
          <==> y == log10(x)/log10(2). 

    (Note: ^ is *NOT* a C++ operator, nor is <==>.)
*/

#include<iostream>
#include<climits>
#include<cmath>
#include<cstdlib>
using std::cout;
using std::cin;
using std::endl;

const int NDIGITS_MAX = static_cast<int>( log10(INT_MAX)/log10(2.0) ) + 1;
int main()
{
     cout << "\nThis program prints out the binary digits "
	  << "of a nonnegative integer.";
     cout << "\nEnter a nonnegative integer (maximum " 
	  << INT_MAX << "): ";
     int number,  count=0;
     bool digits[NDIGITS_MAX];
     cin  >> number;
     if (number < 0){
	cout << "The number must be nonnegative!\n\n";
	return EXIT_FAILURE;
     }

     do {                                 // Store the digits in reverse order
        digits[count] = bool(number%2);   //  in the array called "digits"
	count  = count + 1;
	number = number / 2;
     }while ( number > 0 );
   
     while (count > 0)
     {
       count = count-1;
       cout << int(digits[count]);  // Print out the elements of the 
     }                              // array in reverse order.  Having
     cout << endl << endl;          // reversed the order twice, we obtain the
                                    // digits in the correct, original order.
     return EXIT_SUCCESS;
}

/*  Sample I/O

Script started on Tue Jan 29 09:49:20 2002
whale.1> a.out

This program prints out the binary digits of a nonnegative integer.
Enter a nonnegative integer (maximum 2147483647): -38912
The number must be nonnegative!

whale.2> a.out

This program prints out the binary digits of a nonnegative integer.
Enter a nonnegative integer (maximum 2147483647): 0
0

whale.3> a.out

This program prints out the binary digits of a nonnegative integer.
Enter a nonnegative integer (maximum 2147483647): 3
11

whale.4> a.out

This program prints out the binary digits of a nonnegative integer.
Enter a nonnegative integer (maximum 2147483647): 6
110

whale.5> a.out

This program prints out the binary digits of a nonnegative integer.
Enter a nonnegative integer (maximum 2147483647): 1024
10000000000

whale.6> exit
exit

script done on Tue Jan 29 09:49:40 2002
*/