Difference Between 3NF and BCNF

When it comes to database normalization, distinguishing between the third normal form (3NF) and the Boyce-Codd normal form (BCNF) is essential for ensuring data integrity and efficiency. This article will explore the fundamental disparities between these two normalization forms, shedding light on their strengths and use cases. Whether you are new to database design or seeking a refresher on these concepts, this guide will equip you with the knowledge to make informed decisions when structuring databases.

Understanding the variance between 3NF and BCNF is crucial for database designers and developers. This article delves into the specific dissimilarities between these two normalization forms and provides valuable guidance on their practical implementation.

Table of Content

• Difference Between 3NF and BCNF: 3NF vs BCNF
• What is 3NF?
• What is BCNF?
• Key Difference Between 3NF and BCNF

What is the Difference Between 3NF and BCNF?

Parameter	3NF	BCNF
Definition	A relation is in 3NF if it is in 2NF, and every non-prime attribute is fully functionally dependent on every candidate key.	A relation is in BCNF if every determinant is a candidate key.
Dependency	Eliminates transitive dependencies.	Eliminates all types of dependencies except trivial functional dependencies.
Candidate Keys	Allows for multiple candidate keys.	Allows only one candidate key.
Redundancy	It may contain some redundant data.	Does not contain any redundant data.
Normal Form Level	Stricter than 2NF but less strict than BCNF.	Stricter than 3NF.
Anomalies	Prevents insertion, update, and deletion anomalies.	Prevents all types of anomalies, including those prevented by 3NF.
Decomposition	It may require further decomposition.	No further decomposition is required.
Complexity	Less complex than BCNF.	More complex than 3NF.
Preservation	Preserves data integrity partially.	Preserves data integrity completely.
Practical Use	Widely used in database design.	Used in specific cases where data integrity is critical.

What is 3NF?

3NF (Third Normal Form) is a level of database normalization that eliminates transitive dependencies. A relation is in 3NF if it is in 2NF (Second Normal Form) and every non-prime attribute is fully functionally dependent on every candidate key.

Formula: A relation R is in 3NF if, for every non-trivial functional dependency X → Y, at least one of the following conditions holds:

1. X is a superkey of R.
2. Y is a prime attribute of R.

Example: Consider a table "Students" with the following attributes: (StudentID, StudentName, CourseID, CourseName, DepartmentID, DepartmentName).

The functional dependencies are:

• StudentID → StudentName
• CourseID → CourseName
• DepartmentID → DepartmentName
• CourseID → DepartmentID (Transitive dependency)

To bring the relation into 3NF, we need to remove the transitive dependency by decomposing the relation into two relations:

1. Students (StudentID, StudentName, CourseID, DepartmentID)
2. Courses (CourseID, CourseName, DepartmentID, DepartmentName)

What is BCNF?

BCNF (Boyce-Codd Normal Form) is a higher level of normalization than 3NF. A relation is in BCNF if every determinant is a candidate key. In other words, for every functional dependency X → Y, X must be a superkey of the relation.

Example: Consider the same "Students" table as before:

Students (StudentID, StudentName, CourseID, CourseName, DepartmentID, DepartmentName)

To bring the relation into BCNF, we need to decompose it into three relations:

1. Students (StudentID, StudentName)
2. Courses (CourseID, CourseName, DepartmentID)
3. Departments (DepartmentID, DepartmentName)

In this decomposition, each relation has a single candidate key, and there are no non-trivial functional dependencies between non-key attributes.

Key Difference Between 3NF and BCNF

1. Candidate Keys: In 3NF, a relation can have multiple candidate keys, while in BCNF, a relation can have only one candidate key.
2. Dependency Elimination: 3NF eliminates only transitive dependencies, while BCNF eliminates all types of dependencies except trivial functional dependencies.
3. Redundancy: Relations in 3NF may still contain some redundant data, whereas relations in BCNF do not contain any redundant data.
4. Data Integrity: BCNF provides better data integrity than 3NF by eliminating more types of anomalies, such as update, insertion, and deletion anomalies.
5. Decomposition: Achieving BCNF often requires further decomposition of relations compared to 3NF, potentially resulting in more relations and increased complexity in the database design.

Conclusion

The third normal form (3NF) and Boyce-Codd normal form (BCNF) are essential for ensuring data integrity and efficiency. In this article, we have briefly discussed how 3NF and BCNF are distinct from each other.

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