CHAPTER 1: DATA REPRESENTATION

1.1 USER-DEFINED DATA TYPES

1.1.1 Introduction to User-Defined Data Types

Definition: User-defined data types are data types designed by the programmer. When object-oriented programming is not being used, a programmer may choose to utilize user-defined data types for a large program as their use can reduce errors and make the program more understandable.

Why Use User-Defined Data Types:

• Reduce errors in the program
• Make code more understandable
• Less restriction than built-in types
• Allows for inevitable user definition

1.1.2 Non-Composite User-Defined Data Types

Enumerated Data Type: A non-composite user-defined data type that is a list of possible data values. The values defined have an implied order of values to allow comparisons.

Characteristics:

• Values are countable and finite
• Allow comparisons (value2 > value1)
• NOT string values (don't use quotes)

Pointer Data Type: Used to reference a memory location. It may be used to construct dynamically varying data structures. The pointer definition has to relate to the type of the variable being pointed to.

Pointer Notation:

• @identifier - returns the address of identifier
• Pointer^ - accesses the data stored at the address (dereferencing)

1.1.3 Composite User-Defined Data Types

Record Data Type: A data type that contains a fixed number of components that can be of different types. Allows the programmer to collect values with other data types together when these form a coherent whole.

Set Data Type: Allows a program to create sets and to apply mathematical operations defined in set theory. All elements in the set should be unique.

Operations on Sets:

• Union
• Difference
• Intersection
• Include an element
• Exclude an element
• Check whether an element is in a set

Class (in OOP): In object-oriented programming, a program defines the classes to be used. Then, for each class, the objects must be defined. A Class includes variables and methods (functions or procedures that an object can run).

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1.2 FILE ORGANISATION AND ACCESS

1.2.1 Types of Files

Text Files:

• Contains data stored according to a defined character code (ASCII or Unicode)
• Can be created using a text editor
• Data appears as readable characters

Binary Files:

• Designed for storing data to be used by a computer program
• Stores data in its internal representation
• Created using specific programs
• Structure: File → Records → Fields → Values

1.2.2 Methods of File Organisation

Serial Files:

• Records have no defined order
• Stored one after another in the order they were added
• New records added at the end of the file
• No end of record character (must have defined format)

Advantages:

• Simple task
• Low cost

Disadvantages:

• Difficult to access specific records
• Must read all preceding records
• Cannot support modern high-speed requirements

File Access: Sequential access only

Uses:

• Batch processing
• Backing up data on magnetic tape
• Bank transactions

Sequential Files:

• Records ordered using a key field
• Key field values must be unique and ordered
• More efficient than serial files due to data integrity
• New records must be added in correct position

File Access Methods:

1. Sequential Access: Read key field values until required value found
2. Direct Access: Use index to look up address of record location

Random Files:

• Records stored randomly
• Accessed directly using hashing algorithm
• Uses hashing on record's key field to calculate address
• Well suited for magnetic and optical disks

Advantages:

• Quick retrieval of records
• Records may vary in size

1.2.3 Hashing Algorithms

Definition: Takes the key field as input and outputs a value for the record's position relative to the file's start.

Example:

Handling Collisions: When two different keys produce the same position, use the next available position in the file.

File Access:

• Value in key field submitted to hashing algorithm
• Algorithm provides position in file
• May require short linear search due to collisions

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1.3 FLOATING-POINT NUMBERS

1.3.1 Floating-Point Representation

Definition: The approximate representation of a real number using binary digits.

Format:

• Mantissa: The non-zero part of the number
• Exponent: The power to which the base is raised
• Base: 2 (in binary floating-point)

1.3.2 Converting Denary to Floating-Point Binary

Steps:

1. Convert whole number part to binary
2. Add sign bit (0 for positive, 1 for negative)
3. Convert fractional part by multiplying by 2 and recording whole parts
4. Combine parts and adjust exponent
5. Normalise the number

Example: Converting 8.75 to floating-point (8-bit: 4 for mantissa, 4 for exponent)

1.3.3 Normalisation

Purpose:

• Maximise precision using all available bits in mantissa
• Ensure most significant bits are different (0 1 for positive, 1 0 for negative)
• Avoid multiple representations of the same number

Process:

• For positive numbers: Shift left until first bit after binary point is 1
• For negative numbers: Shift left until first two bits are different (10)
• Each shift left decreases exponent by 1

1.3.4 Problems with Floating-Point Numbers

1. Rounding Errors:

   • Binary representation of fractions is often approximate
   • Can become significant after multiple calculations

2. Overflow:

   • Result too large to represent
   • Occurs when exponent exceeds maximum

3. Underflow:

   • Result too small to represent
   • May be rounded to zero

4. Inability to Store Zero:

   • Normalised form requires mantissa to be 0.1 or 1.0
   • Zero must be handled as special case

1.3.5 Precision vs Range

Trade-off: Must balance precision and range based on application needs