This demonstrates how a binary monetary system is clearly superior to our USD.

3310-binary-coins.cpp

/* {{{
   **************************
   * Mark Holmberg : tiggers.no.tail@gmail.com
   * Purpose: calculate the average number of coins needed to make change
   * Tue Oct 13 15:46:34 MDT 2009
   * CS 3310 : Discrete Math
   * }}} */
#include <iostream>
#include <vector>

/*US dollars*/
#define HALF	50
#define QUARTER 25
#define DIME	10
#define	NICKEL	 5
#define	PENNY	 1
/*Binary System*/
#define SIXTY_FOUR	64
#define	THRTY_TWO	32
#define SIXTEEN		16
#define	EIGHT		 8
#define	FOUR		 4
#define	TWO			 2
#define	ONE			 1

namespace mdh {
	int computeCoins( std::vector<int> coinage_system, int iAmount ) {
		std::vector<int>::iterator it;		//iterator
		double div_result;					//result of division
		int mod_remainder;					//holds the remainder of division
		int num_coins;						//determines how many coins it takes this modulo/division time
		//int original_amount = iAmount;	//iAmount will change, so we want to know what we were passed originally
		int total_coins = 0;				//the total coins

		//iterate through all possible denomination values in the vector
		for( it = coinage_system.begin(); it != coinage_system.end(); it++ ) {
			if( iAmount % (*it) == 0 ) {
				//i.e. 100 is evenly divided into 2 half dollars so count the number of coins
				num_coins = iAmount / (*it);
				if( num_coins > 0 ) { total_coins = total_coins + num_coins; }
				break;	//if we don't have this we get ALL possible combos. we want highest amount coins first
			} else {
				//divide
				div_result = iAmount / (*it);
				if( div_result > 0 ) { total_coins += div_result; }

				//something divided in
				if( div_result != 0 ) {
					num_coins += div_result;
				}
				mod_remainder = iAmount % (*it);	/*find out the remainder*/
				iAmount = mod_remainder;	//only divide by whats left
			}//end else clause
		}//end for loop

		return total_coins;
	}//end computeCoins

	double calculateAverage( double iMyInput ) {
		return iMyInput / 100.0;
	}
}//end mdh namespace

using namespace std;
int main() {
	std::cout.setf(std::ios::fixed);	//sets the level of precision
//--------------------------------------------------
// American US Monetary System
//--------------------------------------------------
	std::vector<int> US_SYSTEM;
	double us_average = 0;

	US_SYSTEM.push_back( HALF );
	US_SYSTEM.push_back( QUARTER );
	US_SYSTEM.push_back( DIME );
	US_SYSTEM.push_back( NICKEL );
	US_SYSTEM.push_back( PENNY );

	for( int i = 100; i > 1; i-- ) {
		int temp = mdh::computeCoins( US_SYSTEM, i );
		us_average += temp;
	}

	us_average = mdh::calculateAverage( us_average );
	std::cout << "American English System average is: " << us_average << std::endl;
//--------------------------------------------------
//--------------------------------------------------
//Binary Monetary System
//--------------------------------------------------
	std::vector<int> BINARY_SYSTEM;
	double binary_average = 0;

	BINARY_SYSTEM.push_back( SIXTY_FOUR );
	BINARY_SYSTEM.push_back( THRTY_TWO );
	BINARY_SYSTEM.push_back( SIXTEEN );
	BINARY_SYSTEM.push_back( EIGHT );
	BINARY_SYSTEM.push_back( FOUR );
	BINARY_SYSTEM.push_back( TWO );
	BINARY_SYSTEM.push_back( ONE );

	for( int k = 100; k > 1; k-- ) {
		int not_temp = mdh::computeCoins( BINARY_SYSTEM, k );
		binary_average += not_temp;
	}

	binary_average = mdh::calculateAverage( binary_average );
	std::cout << "Binary System average is: " << binary_average << std::endl;
//--------------------------------------------------

	return 0;
}