Normalisation is essential to database administration because it guarantees data economy, scalability, and integrity. Database Normal Forms are a collection of guidelines that control how data is arranged in relational databases to maximise efficiency and reduce dependencies and redundancies. From First Normal Form (1NF) to Sixth Normal Form (6NF), we shall examine the nuances of each Normal Form in this article, including thorough justifications and instructive examples.

First Normal Form (1NF)

The First Normal Form (1NF) is the fundamental building block of database normalization. To meet the requirements of 1NF, a relation must have:

• Atomic Values: Each attribute or field within a relation must hold atomic values, meaning they cannot be further divided.
• Unique Column Names: Every column in a relation must have a unique name to avoid ambiguity.
• No Duplicate Rows: Each row in a relation must be unique, with no duplicate tuples.

Example:

Consider the following table representing student information:

Student_ID	Name	Courses
001	John	Math, Physics
002	Alice	Chemistry, Math
003	Bob	Physics, Biology

To convert this table into 1NF, we need to ensure atomicity and eliminate repeating groups. One way to achieve this is by creating separate rows for each course taken by a student:

Student_ID	Name	Course
001	John	Math
001	John	Physics
002	Alice	Chemistry
002	Alice	Math
003	Bob	Physics
003	Bob	Biology

Second Normal Form (2NF)

Second Normal Form (2NF) builds upon 1NF by addressing partial dependencies within relations. A relation is in 2NF if it meets the following criteria:

• It is in 1NF.
• All non-key attributes are fully functionally dependent on the primary key.

Example:

Consider a table that records orders and their corresponding products:

Order_ID	Product_ID	Product_Name	Unit_Price
1001	001	Laptop	$800
1001	002	Mouse	$20
1002	001	Laptop	$800
1003	003	Keyboard	$50

In this table, Order_ID serves as the primary key, and Product_ID is a partial key. To achieve 2NF, we need to separate the product information into a separate table:

Third Normal Form (3NF)

Third Normal Form (3NF) further refines the normalization process by eliminating transitive dependencies. A relation is in 3NF if it satisfies the following conditions:

• It is in 2NF.
• There are no transitive dependencies; that is, no non-key attribute depends on another non-key attribute.

Example:

Consider a table that stores information about employees, including their department and location:

Employee_ID	Employee_Name	Department	Location
001	John	Marketing	New York
002	Alice	HR	Los Angeles
003	Bob	Marketing	New York

In this table, both Department and Location are non-key attributes. However, Location depends on Department, creating a transitive dependency. To normalize this table to 3NF, we split it into two:

Boyce-Codd Normal Form (BCNF)

Boyce-Codd Normal Form (BCNF) is an extension of 3NF, addressing certain anomalies that may arise in relations with multiple candidate keys. A relation is in BCNF if, for every non-trivial functional dependency X → Y, X is a superkey.

Example:

Consider a table representing courses and their instructors:

Course_ID	Instructor_ID	Instructor_Name	Course_Name
001	101	John	Math
002	102	Alice	Physics
001	103	Bob	Math

In this table, {Course_ID, Instructor_ID} is a composite primary key. However, Instructor_Name depends only on Instructor_ID, violating BCNF. To normalize this table, we separate the Instructor information:

Fifth Normal Form (5NF)

Fifth Normal Form (5NF), also known as Project-Join Normal Form (PJNF), addresses multi-valued dependencies within relations. A relation is in 5NF if it satisfies the following conditions:

• It is in 4NF.
• All join dependencies are implied by the candidate keys.

Example:

Consider a table that represents the relationship between authors and their published books:

Author_ID	Book_ID	Author_Name	Book_Title
101	001	John	Book1
101	002	John	Book2
102	001	Alice	Book1
103	003	Bob	Book3

In this table, {Author_ID, Book_ID} forms a composite primary key. However, there is a multi-valued dependency between Author_ID and Book_Title. To normalize this table to 5NF, we split it into two:

Sixth Normal Form (6NF)

Sixth Normal Form (6NF), also known as Domain-Key Normal Form (DK/NF), deals with cases where dependencies exist between attributes and subsets of the keys. A relation is in 6NF if it meets the following criteria:

• It is in 5NF.
• There are no non-trivial join dependencies involving subsets of the candidate keys.

Example:

Consider a table representing sales data for products:

Product_ID	Product_Name	Region	Sales
001	Laptop	East	$500
001	Laptop	West	$700
002	Mouse	East	$100
002	Mouse	West	$150

In this table, {Product_ID, Region} is a composite key. However, there is a non-trivial join dependency between Region and Sales, as Sales depend only on Region. To normalize this table to 6NF, we separate the Region and Sales information.

Conclusion

To sum up, database normalisation is an essential step in creating relational databases that are effective and easy to maintain. Database designers can minimise redundancy, stop data abnormalities, and improve query efficiency by following the guidelines of Normal Forms. Comprehending and utilising the many Normal Forms, ranging from 1NF to 6NF, equips database experts to develop resilient and expandable database structures that satisfy the dynamic requirements of contemporary applications.