# Normalization

## First Normal Form (1NF)

Each column is unique in 1NF.
As per the rule of first normal form, an attribute (column) of a table cannot hold multiple values. It should hold only atomic values.
Example: 1
Sample Employee table, it displays employees are working with multiple departments.

 Employee Age Department Melvin 32 Marketing, Sales Edward 45 Quality Assurance Alex 36 Human Resource

Employee table following 1NF:

 Employee Age Department Melvin 32 Marketing Melvin 32 Sales Edward 45 Quality Assurance Alex 36 Human Resource

Example 2: Suppose a company wants to store the names and contact details of its employees. It creates a table that looks like this:

 emp_id emp_name emp_address emp_mobile 101 Herschel New Delhi 8912312390 102 Jon Kanpur 8812121212 9900012222 103 Ron Chennai 7778881212 104 Lester Bangalore 9990000123 8123450987

this table is not in 1NF as the rule says “each attribute of a table must have atomic (single) values”, the emp_mobile values for employees Jon & Lester violates that rule.
To make the table complies with 1NF we should have the data like this:

 emp_id emp_name emp_address emp_mobile 101 Herschel New Delhi 8912312390 102 Jon Kanpur 8812121212 102 Jon Kanpur 9900012222 103 Ron Chennai 7778881212 104 Lester Bangalore 9990000123 104 Lester Bangalore 8123450987

Example:- 3

Student Table :

 Student Age Subject Adam 15 Biology, Maths Alex 14 Maths Stuart 17 Maths

In First Normal Form, any row must not have a column in which more than one value is saved, like separated with commas. Rather than that, we must separate such data into multiple rows.
Student Table following 1NF will be :

 Student Age Subject Adam 15 Biology Adam 15 Maths Alex 14 Maths Stuart 17 Maths

Using the First Normal Form, data redundancy increases, as there will be many columns with same data in multiple rows but each row as a whole will be unique.

## Second Normal Form (2NF)

The entity should be considered already in 1NF and all attributes within the entity should depend solely on the unique identifier of the entity.
Example: 1  Sample Products table:

 productID product Brand 1 Monitor Apple 2 Monitor Samsung 3 Scanner HP 4 Head phone JBL

Product table following 2NF:
Products Category table:

 productID product 1 Monitor 2 Scanner 3 Head phone

Brand table:

 brandID Brand 1 Apple 2 Samsung 3 HP 4 JBL

Products Brand table:

 pbID productID brandID 1 1 1 2 1 2 3 2 3 4 3 4

Example 2: Suppose a school wants to store the data of teachers and the subjects they teach. They create a table that looks like this: Since a teacher can teach more than one subjects, the table can have multiple rows for a same teacher.

 teacher_id Subject teacher_age 111 Maths 38 111 Physics 38 222 Biology 38 333 Physics 40 333 Chemistry 40

Candidate Keys: {teacher_id, subject}
Non prime attribute: teacher_age
he table is in 1 NF because each attribute has atomic values. However, it is not in 2NF because non prime attribute teacher_age is dependent on teacher_id alone which is a proper subset of candidate key. This violates the rule for 2NF as the rule says “no non-prime attribute is dependent on the proper subset of any candidate key of the table”.
To make the table complies with 2NF we can break it in two tables like this:
teacher_details table:

 teacher_id teacher_age 111 38 222 38 333 40

teacher_subject table:

 teacher_id Subject 111 Maths 111 Physics 222 Biology 333 Physics 333 Chemistry

Now the tables comply with Second normal form (2NF).

## Third Normal form (3NF)

A table design is said to be in 3NF if both the following conditions hold:

• Table must be in 2NF
• Transitive functional dependency of non-prime attribute on any super key should be removed.

An attribute that is not part of any candidate key is known as non-prime attribute.
In other words 3NF can be explained like this: A table is in 3NF if it is in 2NF and for each functional dependency X-> Y at least one of the following conditions hold:

• X is a super key of table
• Y is a prime attribute of table

An attribute that is a part of one of the candidate keys is known as prime attribute.
Example: Suppose a company wants to store the complete address of each employee, they create a table named employee_details that looks like this:

 emp_id emp_name emp_zip emp_state emp_city emp_district 1001 John 282005 UP Agra Dayal Bagh 1002 Ajeet 222008 TN Chennai M-City 1006 Lora 282007 TN Chennai Urrapakkam 1101 Lilly 292008 UK Pauri Bhagwan 1201 Steve 222999 MP Gwalior Ratan

Super keys: {emp_id}, {emp_id, emp_name}, {emp_id, emp_name, emp_zip}…so on
Candidate Keys: {emp_id}
Non-prime attributes: all attributes except emp_id are non-prime as they are not part of any candidate keys.
Here, emp_state, emp_city & emp_district dependent on emp_zip. And, emp_zip is dependent on emp_id that makes non-prime attributes (emp_state, emp_city & emp_district) transitively dependent on super key (emp_id). This violates the rule of 3NF.
To make this table complies with 3NF we have to break the table into two tables to remove the transitive dependency:
employee table:

 emp_id emp_name emp_zip 1001 John 282005 1002 Ajeet 222008 1006 Lora 282007 1101 Lilly 292008 1201 Steve 222999

employee_zip table:

 emp_zip emp_state emp_city emp_district 282005 UP Agra Dayal Bagh 222008 TN Chennai M-City 282007 TN Chennai Urrapakkam 292008 UK Pauri Bhagwan 222999 MP Gwalior Ratan

## Boyce Codd normal form (BCNF)

It is an advance version of 3NF that’s why it is also referred as 3.5NF. BCNF is stricter than 3NF. A table complies with BCNF if it is in 3NF and for every functional dependency X->Y, X should be the super key of the table.
Example: Suppose there is a company wherein employees work in more than one department. They store the data like this:

 emp_id emp_nationality emp_dept dept_type dept_no_of_emp 1001 Austrian Production and planning D001 200 1001 Austrian stores D001 250 1002 American design and technical support D134 100 1002 American Purchasing department D134 600

Functional dependencies in the table above:
emp_id -> emp_nationality
emp_dept -> {dept_type, dept_no_of_emp}
Candidate key: {emp_id, emp_dept}
The table is not in BCNF as neither emp_id nor emp_dept alone are keys.
To make the table comply with BCNF we can break the table in three tables like this:
emp_nationality table:

 emp_id emp_nationality 1001 Austrian 1002 American

emp_dept table:

 emp_dept dept_type dept_no_of_emp Production and planning D001 200 Stores D001 250 design and technical support D134 100 Purchasing department D134 600

emp_dept_mapping table:

 emp_id emp_dept 1001 Production and planning 1001 Stores 1002 design and technical support 1002 Purchasing department

Functional dependencies:
emp_id -> emp_nationality
emp_dept -> {dept_type, dept_no_of_emp}
Candidate keys:
For first table: emp_id
For second table: emp_dept
For third table: {emp_id, emp_dept}
This is now in BCNF as in both the functional dependencies left side part is a key.