Question
Another major use of shift operations is to pack small integer quantities into a larger unit. For example, a standard Gregorian calendar date contains three integer values: month, day, and year. However, these are all relatively small in relationship to what can be stored in an integer. Given four-byte integers (standard in Visual Studio), storing a date requires twelve bytes (three items times four bytes each).

With the ridiculously low price of memory, one may be tempted to say "so what?" But if one must store many, many dates, this adds up over time. As a result, software designers often search for ways to reduce the size of data items which have many instances.

The example we will use is the Microsoft File Allocation Table system, variously known as FAT16, FAT32, et cetera. The FAT systems arose in the days of 360KB floppy disks and 30MB hard drives. Space usage was obviously more of a critical factor at that time. So, to store dates, Microsoft introduced a date format which incorporated three values in one 16-bit (C++ short data type) value:

Month -4 bits
Month, value 1 through 12
Day - 5 bits
Day of month, value 1 through 31
Year - 7 bits
Year expressed as an offset past 1980, value 0 through 127
The FAT systems officially store date values from 1980-01-01 to 2099-12-31. (The actual limit is 2107-12-31.)
Why did they do this? Well, there was no need to store historical dates, since PCs did not exist before the 1980s. The need to establish a starting date is one of the characteristics of computer time systems.

Your lab exercise for this week is to prepare a program which will convert a 16-bit hexadecimal value into month, day, and year using the above FAT format. You should code the original date as a C++ short value. Here are two values for testing:
• 0x1b62
• 0x1c99

Once you have done this, your Lab Assignment will be to write a program which takes a user-supplied date and produces the corresponding FAT-encoded value. Prompt the user for a month, day, and year. Reject invalid month and day values and end the program with an error message. Reject any year not between 1980 and 2107 and end the program. Produce your output in hexadecimal.

Sample Execution:
CS Lab Assignment 2       [Your Name]

Enter a month, day, and year between 1-1-1980 and 12-31-2107: 3 2 2018
The hexadecimal FAT date is: 2662
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#include <iostream>
#include <iomanip>

using namespace std;

int main(){
short m, d, y;
short date;

cout << "CS 546 Section 14860" << setw(30) << setfill(' ') << "Lab Assignment 2" << setw(30) << "[Your Name]" << endl;
cout << "Enter a month, day, and year between 1-1-1980 and 12-31-2107: ";
cin >> m >> d >> y;

if(m < 1 && m > 12){
cout << "Invalid month";
return 0;
}
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      • Illuminate\Cache\Events\CacheHit (164μs)
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        Backtrace
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        3.61mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        1.35mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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        21.94mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
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        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `subjects` where `subjects`.`id` in (16)
        1.47mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 37394 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.24mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
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        Backtrace
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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