Database Normalization

Database Normalization

Normal Form

The normal forms (abbrev. NF) of relational database theory provide criteria for determining a table’s degree of vulnerability to logical inconsistencies and anomalies. The higher the normal form applicable to a table, the less vulnerable it is to such inconsistencies and anomalies. Each table has a “highest normal form” (HNF): by definition, a table always meets the requirements of its HNF and of all normal forms lower than its HNF; also by definition, a table fails to meet the requirements of any normal form higher than its HNF.

The normal forms are applicable to individual tables; to say that an entire database is in normal form n is to say that all of its tables are in normal form n.

Newcomers to database design sometimes suppose that normalization proceeds in an iterative fashion, i.e. a 1NF design is first normalized to 2NF, then to 3NF, and so on. This is not an accurate description of how normalization typically works. A sensibly designed table is likely to be in 3NF on the first attempt; furthermore, if it is 3NF, it is overwhelmingly likely to have an HNF of 5NF. Achieving the “higher” normal forms (above 3NF) does not usually require an extra expenditure of effort on the part of the designer, because 3NF tables usually need no modification to meet the requirements of these higher normal forms.

Edgar F. Codd originally defined the first three normal forms (1NF, 2NF, and 3NF). These normal forms have been summarized as requiring that all non-key attributes be dependent on “the key, the whole key and nothing but the key”. The fourth and fifth normal forms (4NF and 5NF) deal specifically with the representation of many-to-many and one-to-many relationships among attributes. Sixth normal form (6NF) incorporates considerations relevant to temporal databases.

First Normal Form

A table is in first normal form (1NF) if and only if it faithfully represents a relation. Given that database tables embody a relation-like form, the defining characteristic of one in first normal form is that it does not allow duplicate rows or nulls. Simply put, a table with a unique key (which, by definition, prevents duplicate rows) and without any nullable columns is in 1NF.

Note that the restriction on nullable columns as a 1NF requirement, as espoused by Chris Date, et. al., is controversial. This particular requirement for 1NF is a direct contradiction to Dr. Codd’s vision of the relational database, in which he stated that “null values” must be supported in a fully relational DBMS in order to represent “missing information and inapplicable information in a systematic way, independent of data type.” By redefining 1NF to exclude nullable columns in 1NF, no level of normalization can ever be achieved unless all nullable columns are completely eliminated from the entire database. This is in line with Date’s and Darwen’s vision of the perfect relational database, but can introduce additional complexities in SQL databases to the point of impracticality.

One requirement of a relation is that every table contain exactly one value for each attribute. This is sometimes expressed as “no repeating groups”. While that statement itself is axiomatic, experts disagree about what qualifies as a “repeating group”, in particular whether a value may be a relation value; thus the precise definition of 1NF is the subject of some controversy. Notwithstanding, this theoretical uncertainty applies to relations, not tables. Table manifestations are intrinsically free of variable repeating groups because they are structurally constrained to the same number of columns in all rows.

Second Normal Form

The criteria for second normal form (2NF) are:

  • The table must be in 1NF.
  • None of the non-prime attributes of the table are functionally dependent on a part (proper subset) of a candidate key; in other words, all functional dependencies of non-prime attributes on candidate keys are full functional dependencies.[7] For example, in an “Employees’ Skills” table whose attributes are Employee ID, Employee Address, and Skill, the combination of Employee ID and Skill uniquely identifies records within the table. Given that Employee Address depends on only one of those attributes – namely, Employee ID – the table is not in 2NF.
  • Note that if none of a 1NF table’s candidate keys are composite – i.e. every candidate key consists of just one attribute – then we can say immediately that the table is in 2NF.

Third Normal Form

The criteria for third normal form (3NF) are:

  • The table must be in 2NF.
  • Every non-prime attribute of the table must be non-transitively dependent on every candidate key. A violation of 3NF would mean that at least one non-prime attribute is only indirectly dependent (transitively dependent) on a candidate key. For example, consider a “Departments” table whose attributes are Department ID, Department Name, Manager ID, and Manager Hire Date; and suppose that each manager can manage one or more departments. {Department ID} is a candidate key. Although Manager Hire Date is functionally dependent on the candidate key {Department ID}, this is only because Manager Hire Date depends on Manager ID, which in turn depends on Department ID. This transitive dependency means the table is not in 3NF.
Walid BaniHani


College of Applied Sciences - Al Rustaq

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