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Define the possible scope of the public library system. A single library location that allows a registered library user (card holder) to browse through books, periodicals, and misc multimedia. It would be able rent out those items to the user as well as collect outstanding items from the user.

Simple set of important features:

1) Ability to sign up for a library card (register)

2) Loan out a book

3) Inventory a book

4) Notify a user that a book is overdue.

A more narrow scope based on the features above. (Level 1 decomposition)

A library system would have a:

1) Register a user subsystem - Collect User information from user, create an account, issue a card.

2) Loan out a book subsystem - Determine if the book is in stock, determine if the book is on hold, determine if the book is meant to be checked out, set book/item to a "rented" status.

3) Inventory a book subsystem - Get book from user, set book/items status to "available"

4) Notify user book is overdue subsystem - Check if all books are accounted, issue overdue notice, look up users information, send notice to user.

The two techniques that can be employed in such a system is decomposition (breaking down a system into its smaller subsystems like we just did) and loose coupling (one subystem is not dependent on another one to function)

To get the idea of a multi-layer architecture, use the idea of decomposition. The further you break a system down into its parts, the deeper in the layers you go.

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