Boyce-Codd Normal Form (BCNF) is a database normalization technique used to eliminate certain types of data anomalies in relational database design. It is named after Edgar F. Codd and Raymond F. Boyce, who developed the concept in the 1970s.

BCNF is an extension of the third normal form (3NF) and addresses a specific type of functional dependency called the “nontrivial functional dependency.” A nontrivial functional dependency occurs when a non-prime attribute (an attribute that is not part of any candidate key) depends on a candidate key of the table.

To understand BCNF, let’s first define some key terms:

- Functional Dependency: It is a relationship between two sets of attributes in a relation (table), where the value of one attribute determines the value of another attribute.
- Candidate Key: It is a minimal set of attributes that can uniquely identify each tuple (row) in a relation.

The key idea behind BCNF is that every non-trivial functional dependency in a table should be determined by the candidate key, rather than by any subset of the candidate key. In other words, every non-prime attribute should be functionally dependent on the whole candidate key, not just a part of it.

To convert a table into BCNF, the following conditions must be satisfied:

- The table must be in 3NF.
- For every non-trivial functional dependency, X → Y, X must be a superkey (a set of attributes that can uniquely identify a tuple) of the table.

If a table violates the BCNF conditions, it can be decomposed into multiple tables that satisfy the BCNF requirements. This decomposition involves creating separate tables for each subset of attributes that form a candidate key and the attributes that depend on them. The resulting tables will be free of update anomalies, ensuring data integrity and eliminating redundancy.

It’s important to note that achieving BCNF doesn’t guarantee the absence of all types of anomalies. Other normalization forms, such as fourth normal form (4NF) and fifth normal form (5NF), address further types of dependencies and provide more advanced levels of normalization. The choice of normalization form depends on the specific requirements and characteristics of the database schema.

### Example of Boyce Codd normal form (BCNF):

Let’s consider an example to illustrate the Boyce-Codd Normal Form (BCNF) concept.

Suppose we have a relation (table) called “Students” with the following attributes:

- StudentID (primary key)
- CourseID (primary key)
- StudentName
- CourseName
- InstructorName

The functional dependencies in this relation are as follows:

- StudentID → StudentName
- CourseID → CourseName, InstructorName

Based on the functional dependencies, we can see that both StudentID and CourseID are candidate keys because they uniquely identify each tuple.

However, the table does not satisfy BCNF because the attribute StudentName depends on the partial key StudentID. In BCNF, every non-trivial functional dependency should be determined by the whole candidate key.

To bring the table into BCNF, we can decompose it into two separate tables: “Students” and “Courses.”

Table 1: Students

- StudentID (primary key)
- StudentName

Table 2: Courses

- CourseID (primary key)
- CourseName
- InstructorName

Now, each table satisfies BCNF:

- In the Students table, the non-prime attribute StudentName is functionally dependent on the whole candidate key StudentID.
- In the Courses table, the non-prime attributes CourseName and InstructorName are functionally dependent on the whole candidate key CourseID.

By decomposing the original table, we have eliminated the partial dependency and ensured that each non-trivial functional dependency is determined by the candidate key of its respective table. This normalization helps maintain data integrity and avoids update anomalies in the database.