Second normal form explained

Second normal form (2NF), in database normalization, is a normal form. A relation is in the second normal form if it fulfills the following two requirements:

It is in first normal form.
It does not have any non-prime attribute that is functionally dependent on any proper subset of any candidate key of the relation (i.e. it lacks partial dependencies). A non-prime attribute of a relation is an attribute that is not a part of any candidate key of the relation.

Put simply, a relation (or table) is in 2NF if:

It is in 1NF and has a single attribute unique identifier (UID)(in which case every non key attribute is dependent on the entire UID), or
It is in 1NF and has a multi-attribute unique identifier, and every regular attribute (not part of the UID) is dependent on all attributes in the multi-attribute UID, not just one attribute (or part) of the UID.

If any regular (non-prime) attributes are predictable (dependent) on another (non-prime) attribute, that is addressed in third normal form.

History

The second normal form was originally defined by E. F. Codd in 1971.^[1]

Decomposition of 1NF into 2NF

To make a 1NF relation a 2NF relation, remove the functionally dependent attributes in the partial dependencies of the first normal form relation, and place those partial dependency dependent attributes in a relation where their corresponding determinant attributes are an entire candidate key.

Example

The following relation does not satisfy 2NF because:

There is a multi-attribute unique identifier: "Manufacturer" and "Model".
is functionally dependent (predictable) on .
is not part of a candidate key, so it is a non-prime attribute. (It is assumed that it is possible for two manufacturers in the same country to make a toothbrush with the same model name, so is not a candidate key even though in the current table the pair uniquely identify rows.)
is a proper subset of the candidate key.

In other words, since is a non-prime attribute functionally dependent on a proper subset of a candidate key, the relation is in violation of 2NF.

Electric toothbrush models! Manufacturer !! Model !! Manufacturer country
Forte	X-Prime	Italy
Forte	Ultraclean	Italy
Dent-o-Fresh	EZbrush	USA
Brushmaster	SuperBrush	USA
Kobayashi	ST-60	Japan
Hoch	Toothmaster	Germany
Hoch	X-Prime	Germany

To make the design conform to 2NF, it is necessary to have two relations. To create these relations:

Remove the functionally dependent attributes in the partial dependencies of the first normal form relation. In this example, is the functionally dependent attribute which will be removed.
Place those partial dependency-dependent attributes (i.e.) in a relation where their corresponding determinant attributes are a candidate key (i.e.).

As seen below, is removed from the original table:

Electric toothbrush models! Manufacturer !! Model
Forte	X-Prime
Forte	Ultraclean
Dent-o-Fresh	EZbrush
Brushmaster	SuperBrush
Kobayashi	ST-60
Hoch	Toothmaster
Hoch	X-Prime

As seen below, the partial dependency is put into a new relation where the dependency can exist without being a partial dependency:

Electric toothbrush manufacturers! Manufacturer !! Manufacturer country
Forte	Italy
Dent-o-Fresh	USA
Brushmaster	USA
Kobayashi	Japan
Hoch	Germany

External links

Database Normalization Basics by Mike Chapple (About.com)
An Introduction to Database Normalization by Mike Hillyer.
A tutorial on the first 3 normal forms by Fred Coulson
Description of the database normalization basics by Microsoft

Notes and References

Codd, E. F. "Further Normalization of the Data Base Relational Model". (Presented at Courant Computer Science Symposia Series 6, "Data Base Systems", New York City, May 24–25, 1971.) IBM Research Report RJ909 (August 31, 1971). Republished in Randall J. Rustin (ed.), Data Base Systems: Courant Computer Science Symposia Series 6. Prentice-Hall, 1972.