1. CSCI 2141 – Intro to Database Systems Database Normalization
3NF and BCNF

2. Converting to 3NF Tables are in 3NF (Third Normal Form) when
They are in 2NF, and
They have no transitive dependencies
Transitive dependency: An attribute functionally depends on another non-key attribute
Converting to 3NF
Ensure that the tables are in 2NF
Make new tables to eliminate transitive dependencies
Reassign corresponding dependent attributes

3. Example Identify all dependencies.
Identify which normal form the table is in.
Convert to the third normal form (3NF).
INV_NUM
INV_DATE
INV_AMOUNT
CUS_NUM
CUS_ADDRESS
CUS_PHONE

4. Example – Solution Dependencies are shown in figure below.
Table is in 1NF as all attributes show functional dependency on the PK
Table is also in 2NF as the PK is not composite, and there is no candidate key.
There are no partial dependencies
INV_NUM
INV_DATE
INV_AMOUNT
CUS_NUM
CUS_ADDRESS
CUS_PHONE
Original table
Transitive Dependencies

5. Example – Solution
Eliminating transitive dependencies result in the following tables
Each of the table above is in 3NF
INV_NUM
INV_DATE
INV_AMOUNT
CUS_NUM
New Tables
CUS_NUM
CUS_ADDRESS
CUS_PHONE

6. Practice Exercise 5 Using the INVOICE table structure shown below:
Write the relational schema, and draw its dependency diagram identifying all dependencies (Assume there are no repeating groups and invoice number references more than one product)
Remove all partial dependencies, write the relational schema, and draw the new dependency diagrams. Identify the normal forms for each table structure you create
Remove all transitive dependencies, write the relational schema, and draw the new dependency diagrams. Also, draw the ERD
Attribute Name
Sample Value
INV_NUM
211347
211348
211349
PROD_NUM
AA-E3422QW
QD X
RU G
GH P
SALE_DATE
15-Jan-2016
16-Jan-2016
PROD_LABEL
Rotary sander
0.25-in. drill bit
Band saw
Power drill
VEND_CODE
211
309
157
VEND_NAME
NeverFail, Inc.
BeGood, Inc.
ToughGo, Inc.
QUANT_SOLD 1 8 2
PROD_PRICE
$49.95
$3.45
$39.99
$87.75
any invoice number may reference more than one product.

7. Practice Exercise 5 – Solution
Relational schema and dependency diagram are as shown

8. Practice Exercise 5 – Solution
Relational schema, and tables with partial dependencies removed (at least 2NF) are as shown below:
We can identify the sale date using the invoice number, but cannot identify the invoice number from the sale date as many invoices are made on any given day

9. Practice Exercise 5 – Solution
Relational schema, and tables with transitive dependencies removed (3NF) are as shown below:

10. Practice Exercise 5 – Solution
ERD is shown below:
the dependency diagrams cannot show the nature (1:1, 1:M, M:N) of the relationships, the ER Diagrams remain crucial to the design effort. Complex design is impossible to produce successfully without some form of modeling

11. Boyce-Codd Normal Form (BCNF)
BCNF is a special case of 3NF
Table is in BCNF when every determinant in the table is a candidate key
When a table in 3NF has only one candidate key, it is also in BCNF
How can a table be in 3NF but not in BCNF?
So in order for the BCNF to be violated, a table must have more than one candidate key, or at least one candidate key other than the primary key
When a table has overlapping candidate keys, it may or may not be in BCNF

12. Boyce-Codd Normal Form (BCNF)
Consider the following table:
Its candidate keys are given to be:
A+B
A+C
Identify its dependencies and determinants
C->B, note that C is a key or prime attribute (or part of a candidate key), and not a non-key attribute

13. Boyce-Codd Normal Form (BCNF)
Is the table in 1NF?
Key (or prime) attributes are defined
All non-key attributes are determined by the key
Is the table in 2NF?
It is in 1NF
No partial dependencies
Is the table in 3NF
It is in 2NF
No transitive dependencies
Note that C → B is not transitive
The table is in 3NF, however, it is not in BCNF
Note that here, key refers to both the PK and the Candidate key
Transitive dependency is defined as the dependency of a non-key attribute on another non-key attribute

14. Boyce-Codd Normal Form (BCNF)
The dependency C → B means that effectively, C is a superset of B
In order to convert to BCNF, change the PK to A+C
Can you identify the normal form for the table below?
1NF

15. Boyce-Codd Normal Form (BCNF)

16. BCNF - Example Table below reflects the following conditions:
A class represents one section of a course (that may have many)
A student can take many classes
A staff member can teach many classes, but one class is taught by one staff member
E.g. student 125 has taken 2 classes, getting A and C grades respectively
Also, using Staff_ID, we cannot determine class_code as one staff may teach many classes (even for the same course), but knowing class_code, we can determine staff_id, hence Class_Code -> Staff_ID

17. BCNF - Example

18. BCNF – Exercise Convert the dependency diagram given below to 3NF
Determine if the 3NF is also in BCNF
If not, convert to BCNF

19. Exercise – Solution Step 1: Removing partial dependencies, we get:
3 NF C E F D B
2 NF
Transitive dependency G
Not a transitive dependency

20. Exercise – Solution
Step 2: Removing transitive dependencies, we get:

21. Exercise – Solution Step 3: Converting to BCNF Change the PK to A+C
Table is now in 1NF due to a partial dependency C →B
Convert table to 3NF
All tables are in 3NF and BCNF