Data Representation : Chapter 13 | Detailed CS 9618 A Level Notes

A Level · Chapter 13

Data Representation

User-defined types · File organisation · Floating-point numbers

🧩 13.1 User-Defined Data Types

Core Idea

Built-in types (INTEGER, STRING…) aren’t always enough. When modelling real-world things, you define your own types — making code clearer, safer, and more self-documenting.

Non-Composite Types

These store a single value, but of a custom kind.

🏷️ Enumerated Type

A fixed list of named values. The compiler assigns integer codes internally.

TYPE Season = (Spring, Summer, Autumn, Winter) DECLARE today : Season today ← Summer

Why use it

Prevents magic numbers. today = 1 is cryptic; today = Summer is readable.

👉 Pointer Type

Stores a memory address rather than a value. Essential for dynamic data structures like linked lists and trees.

TYPE IntPointer = ^INTEGER DECLARE p : IntPointer p ← ^myVar // p holds address // of myVar

Analogy

A pointer is like a Post-It note with a house address written on it — not the house itself, just directions to find it.

Composite Types

These bundle multiple fields or values together.

A record groups related data of different types under one name — like a database row.

TYPE Student DECLARE name : STRING DECLARE age : INTEGER DECLARE grade : REAL ENDTYPE DECLARE s : Student s.name ← “Aisha” s.age ← 17 s.grade ← 91.5

Real world

A school database stores name, DOB, scores together — that’s a record.

A set holds distinct values with no duplicates and no defined order. Supports mathematical set operations.

TYPE LetterSet = SET OF CHAR DECLARE vowels : LetterSet vowels ← {‘a’,’e’,’i’,’o’,’u’} // Operations: // Union: A ∪ B // Intersection: A ∩ B // Difference: A – B

Useful when you need membership testing: Is ‘e’ in vowels?

A class is a blueprint combining data (attributes) and behaviour (methods). An object is an instance of a class.

CLASS BankAccount PRIVATE balance : REAL PUBLIC PROCEDURE deposit(amount : REAL) balance ← balance + amount ENDPROCEDURE PUBLIC FUNCTION getBalance() RETURNS REAL RETURN balance ENDFUNCTION ENDCLASS DECLARE acc : BankAccount acc.deposit(500) OUTPUT acc.getBalance() // 500

Key OOP terms

Encapsulation Inheritance Polymorphism Aggregation Getter / Setter

🗄️ 13.2 File Organisation & Access

How records are physically arranged on disk determines how quickly they can be found.

Method	How records are stored	Access type	Best for
Serial	In order of arrival — no sorting	Sequential only	Log files, backups
Sequential	Sorted by a key field	Sequential or Direct	Batch processing, sorted reports
Random	Address computed via hash of key	Direct (fast!)	Real-time lookups, e.g. bank accounts

Analogy

Serial = pile of unsorted papers. Sequential = alphabetical filing cabinet. Random = indexed database where you jump straight to the right drawer.

Hashing Algorithms

Random files use a hashing function to convert a record key into a storage address.

Address = Key MOD NumberOfSlots Example: Key = 1047, Slots = 100 Address = 1047 MOD 100 = 47 → Store/retrieve record at slot 47

A collision occurs when two different keys hash to the same address.

Solutions:

Linear probing: Try next slot (Address+1, Address+2…) until empty slot found
Chaining: Each slot holds a linked list of records that hash there
Double hashing: Apply a second hash function to find the next probe position

Exam tip

You may be asked to trace through a hash function with linear probing — show each step explicitly.

🔢 13.3 Floating-Point Numbers

Integers can’t represent fractions. Floating-point sacrifices exactness for range by splitting the bits into two parts:

S
1 bit

MANTISSA (significand)
The actual digits / precision

EXPONENT
Scale / magnitude

Value = Mantissa × 2^Exponent

Analogy

Scientific notation: 3.14 × 10² = 314. Mantissa = 3.14, Exponent = 2. Floating-point is exactly this, but in binary.

Two’s Complement in Floating Point

Both mantissa and exponent are stored in two’s complement form.

8-bit format: 5-bit mantissa, 3-bit exponent (both two’s complement)

Binary: 0 1 1 0 1 | 0 1 0 mantissa | exponent Step 1 – Exponent: 010 in two’s complement = +2 Step 2 – Mantissa: 01101 = +0.1101 (normalised, leading .0 or .1) Value = 0.1101₂ Step 3 – Apply exponent (shift point right 2): 0.1101 × 2² = 011.01₂ Step 4 – Convert: 011.01₂ = 3.25₁₀ ✓

Rule

Positive exponent → shift binary point RIGHT. Negative exponent → shift LEFT.

Normalisation

A number is normalised when the mantissa starts with the most significant bit — no leading redundant zeros or ones.

✅ Normalised

Positive: 0.1xxxxxxx (first bit after point = 1) Negative: 1.0xxxxxxx (first bit after point = 0)

❌ Not Normalised

0.0xxxxxxx ← wasted bits! 1.1xxxxxxx ← redundant sign

Leading redundant bits reduce precision — normalisation maximises the meaningful bits in the mantissa.

Mantissa vs Exponent Bits Trade-off

More bits to…	Effect on precision	Effect on range
Mantissa	✅ Higher precision (more decimal places)	❌ Smaller range
Exponent	❌ Lower precision	✅ Larger range (bigger/smaller numbers)

📈 Overflow

Number too large for the exponent bits to represent. Result wraps or becomes infinity.

📉 Underflow

Number too small/close to zero for the exponent. Result rounds to 0 incorrectly.

Rounding errors

Most real numbers can’t be represented exactly in binary. For example, 0.1 in decimal is a repeating fraction in binary (0.0001100110011…). Every time arithmetic is done, tiny errors accumulate. This is why 0.1 + 0.2 ≠ 0.3 in many programming languages!

⚡ Exam Essentials

Know how to convert binary float → denary and back
Normalise a given floating-point number
Explain why binary representations are approximations
Describe consequences of changing mantissa vs exponent allocation

📓 Other Notes:

Chapter 14: Communication & Internet Chapter 15: Hardware & Virtual Machines Chapter 16: System Software Chapter 17: Security Chapter 18: Artificial Intelligence

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