So I have three files all in the same folder: dtime.h, dtime.cpp, and testapp.cpp

dtime.h:

//This is the header file dtime.h. This is the interface for the class DigitalTime.
//Values of this type are times of day. The values are input and output in
//24 hour notation as in 9:30 for 9:30 AM and 14:45 for 2:45 PM.

#ifndef DTIME_H
#define DTIME_H

#include <iostream>
using namespace std;

class DigitalTime
{
public:
    DigitalTime(int theHour, int theMinute);
    DigitalTime( );
    //Initializes the time value to 0:00 (which is midnight).

    int getHour( ) const;
    int getMinute( ) const;
    void advance(int minutesAdded);
    //Changes the time to minutesAdded minutes later.

    void advance(int hoursAdded, int minutesAdded);
    //Changes the time to hoursAdded hours plus minutesAdded minutes later.


    friend bool operator ==(const DigitalTime& time1, 
                            const DigitalTime& time2);

    friend istream& operator >>(istream& ins, DigitalTime& theObject);

    friend ostream& operator <<(ostream& outs, const DigitalTime& theObject);

private:
  
    int hour;
    int minute;
 
    static void readHour(int& theHour);
    //Precondition: Next input in to be read from the keyboard is 
    //a time in notation, like 9:45 or 14:45.
    //Postcondition: theHour has been set to the hour part of the time. 
    //The colon has been discarded and the next input to be read is the minute.

    static void readMinute(int& theMinute);
    //Reads the minute from the keyboard after readHour has read the hour.

    static int digitToInt(char c);
    //Precondition: c is one of the digits ’0’ through ’9’.
    //Returns the integer for the digit; that is, digitToInt(’3’) returns 3.

};


#endif //DTIME_H

dtime.cpp:

//This is the implementation file: dtime.cpp of the class DigitalTime.
//The interface for the class DigitalTime is in the header file dtime.h.
#include <iostream>
#include <cctype>
#include <cstdlib>
using namespace std;
#include "dtime.h"

//Uses iostream and cstdlib:
DigitalTime::DigitalTime(int theHour, int theMinute)
{
    if (theHour < 0 || theHour > 24 || theMinute < 0 || theMinute > 59)
    {
        cout << "Illegal argument to DigitalTime constructor.";
        exit(1);
    }
    else
    {
        hour = theHour;
        minute = theMinute;
    }

    if (hour == 24)
        hour = 0; //standardize midnight as 0:00
}

DigitalTime::DigitalTime( )
{
    hour = 0;
    minute = 0;
}

int DigitalTime::getHour( ) const
{
    return hour;
}

int DigitalTime::getMinute( ) const
{
    return minute;
}

void DigitalTime::advance(int minutesAdded)
{
    int grossMinutes = minute + minutesAdded;
    minute = grossMinutes%60;

    int hourAdjustment = grossMinutes/60;
    hour = (hour + hourAdjustment)%24;
}

void DigitalTime::advance(int hoursAdded, int minutesAdded)
{
    hour = (hour + hoursAdded)%24;
    advance(minutesAdded);
}

bool operator ==(const DigitalTime& time1, const DigitalTime& time2)
{
    return (time1.hour == time2.hour && time1.minute == time2.minute);
}

//Uses iostream:
ostream& operator <<(ostream& outs, const DigitalTime& theObject)
{
    outs << theObject.hour << ':';
    if (theObject.minute < 10)
        outs << '0';
    outs << theObject.minute;
    return outs;
}

//Uses iostream:
istream& operator >>(istream& ins, DigitalTime& theObject)
{
    DigitalTime::readHour(theObject.hour);
    DigitalTime::readMinute(theObject.minute);
    return ins;
}

int DigitalTime::digitToInt(char c)
{
    return ( int(c) - int('0') );
}

//Uses iostream, cctype, and cstdlib:
void DigitalTime::readMinute(int& theMinute)
{
    char c1, c2;
    cin >> c1 >> c2;

    if (!(isdigit(c1) && isdigit(c2)))
    {
        cout << "Error illegal input to readMinute\n";
        exit(1);
    }

    theMinute = digitToInt(c1)*10 + digitToInt(c2);

    if (theMinute < 0 || theMinute > 59)
    {
        cout << "Error illegal input to readMinute\n";
        exit(1);
    }
}

//Uses iostream, cctype, and cstdlib:
void DigitalTime::readHour(int& theHour)
{
    char c1, c2;
    cin >> c1 >> c2;
    if ( !( isdigit(c1) && (isdigit(c2) || c2 == ':' ) ) )
    {
        cout << "Error illegal input to readHour\n";
        exit(1);
    }

    if (isdigit(c1) && c2 == ':')
    {
        theHour = DigitalTime::digitToInt(c1);
    }
    else //(isdigit(c1) && isdigit(c2))
    {
        theHour = DigitalTime::digitToInt(c1)*10 
                  + DigitalTime::digitToInt(c2);
        cin >> c2; //discard ':'
        if (c2 != ':')
        {
            cout << "Error illegal input to readHour\n";
            exit(1);
        }
    }

    if (theHour == 24)
        theHour = 0; //Standardize midnight as 0:00

    if ( theHour < 0 || theHour > 23 )
    {
        cout << "Error illegal input to readHour\n";
        exit(1);
    }
}

testapp.cpp

//This is the application file: timedemo.cpp which demonstrates use of DigitalTime.
#include <iostream>
using namespace std;
#include "dtime.h"

int main( )
{
    DigitalTime clock, oldClock;

    cout << "You may write midnight as either 0:00 or 24:00,\n"
         << "but, I will always write it as 0:00.\n"
         << "Enter the time in 24 hour notation: ";
    cin >> clock;

    oldClock = clock;
    clock.advance(15);
    if (clock == oldClock)
        cout << "Something is wrong.";
    cout << "You entered " << oldClock << endl;
    cout << "15 minutes later the time will be "
         << clock << endl;

    clock.advance(2, 15);
    cout << "2 hours and 15 minutes after that\n"
         << "the time will be "
         << clock << endl;

    return 0;
}

I'm wondering where I'm supposed to put them in MS Visual Studio 2010? Do I put dtime.h in the header file subsection of the project or do I put all of them in the same folder (source files)? They all compile perfectly but the program is not running the way its supposed to. It asks me to enter the time in 24 hour time and I input something like 12:30 and the program ends????????

If it compiles 'perfectly' the files are in the proper folder. You should usually assume on a perfect compile that the error is with code, not the compiler.

After you enter a number, why shouldn't the program end? What statements are there to keep the program running?

I believe the correct description of your problem is that after you enter your time, the program seems to run but upon exit the window closes immediately so you can't see the answer.

Add a cin statement before the ending return to prevent the program from exiting immediately.

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