Back to Curriculum

1. Data Representation

SECTION 1: THEORY FUNDAMENTALS

Data representation is fundamental to understanding how computers store and process information. This chapter covers number systems, character encoding, image representation, sound sampling, and data compression techniques.

Table of Contents

⚠️

Important Note for IGCSE Students

⚠️ IGNORE OCTAL - NOT IN SYLLABUS

The Octal number system (base 8) is NOT part of the IGCSE O-Level Computer Science syllabus. While it may appear in some reference materials or examples, you should focus only on Binary, Decimal, and Hexadecimal for your exam preparation.

You will NOT be tested on Octal conversions or Octal-related questions in the IGCSE exam.

1.1 Number Systems

Key Concepts

Computers use binary (base 2) to represent all data. Understanding how to convert between binary, denary (base 10), and hexadecimal (base 16) is essential for computer science.

Number System Conversion Chart showing conversions between Binary, Denary, and Hexadecimal

Understanding the Number System Diagram

1

Decimal as the Central Number System

The decimal number system (base 10) is placed at the center because it is the system humans use in daily life.

Converting from Decimal:

  • •Decimal → Binary: Convert by repeatedly dividing by 2
  • •Decimal → Octal: Convert by repeatedly dividing by 8
  • •Decimal → Hexadecimal: Convert by repeatedly dividing by 16

Converting back to Decimal:

  • •Binary uses powers of 2
  • •Octal uses powers of 8
  • •Hexadecimal uses powers of 16

Key Insight: This highlights that each number system is based on its base value.

2

Binary as the Foundation of Computing

The binary number system (base 2) is fundamental because computers operate using only 0s and 1s.

The diagram shows how binary connects easily to:

  • •Octal (base 8) by grouping binary digits in groups of 3
  • •Hexadecimal (base 16) by grouping binary digits in groups of 4

Why these groupings work:

8 = 2³ (3 binary digits = 1 octal digit)
16 = 2⁴ (4 binary digits = 1 hexadecimal digit)

Key Insight: This allows direct conversion between binary and hexadecimal without using decimal.

3

Purpose of Octal and Hexadecimal

Octal and Hexadecimal are included to show how large binary numbers can be written in a shorter and more readable form.

  • •Octal compresses binary into groups of 3 bits
  • •Hexadecimal compresses binary into groups of 4 bits

Real-World Application: Hexadecimal is especially important in memory addressing, machine code, and low-level programming.

Number System Comparison Table (0-15)

DecimalHexadecimalBinary (4-bit)
000000
110001
220010
330011
440100
550101
660110
770111
881000
991001
10A1010
11B1011
12C1100
13D1101
14E1110
15F1111

Note: Notice how each hexadecimal digit (0-F) corresponds exactly to a 4-bit binary pattern. This makes conversion between binary and hexadecimal straightforward by grouping binary digits in sets of 4.

Binary (Base 2)

Binary uses only two digits: 0 and 1. Each position represents a power of 2.

Binary to Denary Conversion

To convert binary to denary, multiply each digit by its position value (power of 2) and sum:

Example: 10112
1 × 2³ = 1 × 8 = 8
0 × 2² = 0 × 4 = 0
1 × 2¹ = 1 × 2 = 2
1 × 2⁰ = 1 × 1 = 1
Total = 1110

Denary to Binary Conversion

Repeatedly divide by 2 and collect remainders:

Example: Convert 2510 to binary
25 ÷ 2 = 12 remainder 1
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Read remainders from bottom: 110012

8-bit Binary Range

•Largest denary value in 8-bit: 255 (all 8 bits are 1s: 111111112)
•Smallest denary value in 8-bit: 0 (all 8 bits are 0s: 000000002)
Practice Question
Past Paper

The hockey club wants to increase the number of people that can watch each match to 2000. The 8-bit binary register may no longer be able to store the value.

Give the smallest number of bits that can be used to store the denary value 2000.

Answer:

11 bits

Explanation: To find the smallest number of bits needed, we calculate 2n ≥ 2000. 210 = 1024 (too small), 211 = 2048 (can store values up to 2047, which includes 2000). Therefore, 11 bits is the minimum needed.

Uses of Binary

Why do computer systems use binary to represent data?

Computers use electronic circuits/Logic Gates that recognize only two voltage levels:

  • •High voltage (1) → ON state
  • •Low voltage (0) → OFF state
Two examples of how computer systems use binary to store different forms of data:
  1. Images – Stored using binary pixel values, where each pixel color is represented in binary (e.g., 8-bit color, 24-bit RGB).
  2. Audio Files – Sound waves are converted into binary samples using digital sampling techniques (e.g., MP3 files).

Hexadecimal (Base 16)

Hexadecimal uses 16 digits: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). It's commonly used in computing because it's more compact than binary and easy to convert.

Hexadecimal to Denary

Example: 2A16
2 × 16¹ = 2 × 16 = 32
A × 16⁰ = 10 × 1 = 10
Total = 4210

Binary to Hexadecimal

Group binary digits into groups of 4 (from right), then convert each group:

Example: 101011002
Group: 1010 | 1100
1010₂ = 10₁₀ = A₁₆
1100₂ = 12₁₀ = C₁₆
Result: AC16

Tip: Hexadecimal is often prefixed with "0x" (e.g., 0x2A) or suffixed with "h" (e.g., 2Ah) in programming.

DenaryBinaryHexadecimal
000
111
2102
3113
41004
51015
101010A
151111F
161000010
25511111111FF

Additional Conversion Examples

Example: Convert 45 (Decimal) to Binary

45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Answer (Bottom to Top): 45 in Binary = 1011012

Example: Convert 101101 (Binary) to Decimal

1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 32 + 0 + 8 + 4 + 0 + 1
= 45 (Decimal)

Example: Convert 2F (Hex) to Decimal

2 × 16¹ + F (15) × 16⁰
= 2 × 16 + 15 × 1
= 32 + 15
= 47 (Decimal)

Uses of the Hexadecimal System

  • ✓One hex digit represents 4 binary digits
  • ✓Easier for humans to read, copy, and work with

1. Error Codes (Hex)

Used for debugging programs & memory addressing.

Example: Windows error code 0xC0000005

2. MAC Addresses (Hex)

Identifies devices uniquely on a network.

Example: 00-1C-B3-4F-25-FE

3. IP Addresses (Hex)

IPv4: 192.168.1.1 or C0.A8.01.01 (Hex)

IPv6: a8fb:7a88:fff0:0fff:3d21:2085:66fb:f0fa

4. HTML Color Codes

Used in web development for defining colors.

#FF0000 → Red
#00FF00 → Green
#0000FF → Blue

📝 Exam Keywords

Why a programmer may use hexadecimal to represent binary numbers:

  • • Easier/quicker to understand/read/write
  • • Easier/quicker to debug
  • • Shorter representation (takes up less screen space)

Binary Operations

Binary Addition (8-bit)

Normal Example:

00101101(45 in decimal)
+ 00010111(23 in decimal)
01000000(68 in decimal ✓)
Overflow Example:
01011011 (91 in decimal)
+ 11001010 (202 in decimal)
00100101 (Overflow occurs, result incorrect)

Overflow happens when the sum exceeds 8 bits!

Binary Shifting (8-bit)

Largest number representation in binary shifting

Example of Left Shift (×2) and Right Shift (÷2):

Before:
00001101(13 in decimal)
Left Shift:
00011010(26 in decimal)
Right Shift:
00000110(6 in decimal)

Left shift multiplies, right shift divides. Overflow can occur in left shift.

Binary shifting overflow tip: Left shift multiplies, right shift divides. Overflow can occur in left shift.

This diagram shows how left shift and right shift operations work in binary. A left shift multiplies the number by 2 for each shift, while a right shift divides the number by 2, ignoring any remainder.

Binary shifting overflow example

When a number is shifted left and the result exceeds the fixed bit limit (8 bits), the extra bit is lost, causing an overflow. As a result, the stored value becomes incorrect even though the operation is valid.

Negative Binary Representation (Two's Complement)

To represent negative numbers in binary, use two's complement:

  1. Write the positive number in binary
  2. Invert the bits (flip 0 to 1, 1 to 0)
  3. Add 1 to the result
Two's complement representation of negative numbers in binary

This diagram explains how two's complement is used to represent negative numbers in binary. To represent −12, we first write +12 in binary, then subtract it from 128 (for an 8-bit system) to get 116. Finally, the most significant bit (MSB) is set to 1, which represents −128. Adding −128 and 116 gives −12, showing how negative values are stored using two's complement.

Example: Convert -13 to 8-bit two's complement:

13 in binary:
00001101
Invert bits:
11110010
Add 1:
11110011(-13 in two's complement)
Working of negative number representation in binary using two's complement

This diagram shows the second method of finding two's complement using the flip-and-add approach. First, the positive number (12) is written in 8-bit binary. All bits are then flipped (0 → 1, 1 → 0) to form the one's complement. Next, 1 is added to obtain the two's complement representation. The MSB becomes 1, indicating a negative number. This final binary value correctly represents −12.

📝 Exam Tip: This flip-and-add method is the most commonly used method in exams and real computer systems. Make sure you master this approach!

1.2 Text, Sound and Images

Character Sets

How Text is Stored in a Computer

1. Computers Understand Only Binary

A computer can only process binary digits (0s and 1s). All information, including text, numbers, and symbols, is ultimately represented in binary form.

2. Character Encoding Systems

Text is stored using a character encoding system such as ASCII or Unicode. Each character (letter, number, symbol) is assigned a unique numeric code, which is then stored as a binary value inside the computer.

3. Example: ASCII Encoding
Character: 'A' (uppercase A)
ASCII value: 65
Binary representation: 1000001 (7 or 8 bits)
4. Process of Storing Text
  1. Each character is converted into its numeric code
  2. The numeric code is then converted into binary digits
  3. The computer stores the binary values in memory
  4. When displayed, the binary values are mapped back to their corresponding characters

A character set is a system that computers use to store and represent text in binary format/denary. Each character (letter, number, or symbol) is assigned a unique binary code/Denary Number.

ASCII (American Standard Code for Information Interchange)

ASCII is a character encoding system that assigns a unique Denary/binary code to each character, allowing computers to represent text using 7-bit or 8-bit codes.

  • •Introduced in 1963, updated in 1986
  • •Uses 7-bit codes (128 characters: 0-127 in decimal, 00-7F in hexadecimal)
  • •Includes English letters, numbers, symbols, and control codes
  • •Examples: Lowercase 'a' = 97, Uppercase 'A' = 65
Process of Storing Text
  1. Each character is converted into its numeric code.
  2. The numeric code is then converted into binary digits.
  3. The computer stores the binary values in memory.
  4. When displayed, the binary values are mapped back to their corresponding characters.

✅ So, text in a computer is nothing but a sequence of binary codes representing characters.

Extended ASCII (8-bit)
  • • Uses 8 bits (256 characters: 0-255 in decimal, 00-FF in hex)
  • • Supports non-English alphabets and graphic symbols
  • • Limitation: ASCII does not support non-Western languages (e.g., Chinese, Arabic, Hindi)
ASCII Character Table (Standard 7-bit ASCII: 0-127)
DecHexCharDecHexCharDecHexCharDecHexChar
000NUL707BEL808BS909TAB
100ALF130DCR271BESC3220SP
48300493115032251333
52344533555436655377
5638857399
6541A6642B6743C6844D
6945E7046F7147G7248H
7349I744AJ754BK764CL
774DM784EN794FO8050P
8151Q8252R8353S8454T
8555U8656V8757W8858X
8959Y905AZ
9761a9862b9963c10064d
10165e10266f10367g10468h
10569i1066Aj1076Bk1086Cl
1096Dm1106En1116Fo11270p
11371q11472r11573s11674t
11775u11876v11977w12078x
12179y1227Az
3321!3422"3523#3624$
3725%3826&3927'4028(
4129)422A*432B+442C,
452D-462E.472F/583A:
593B;603C<613D=623E>
633F?6440@915B[925C\
935D]945E^955F_9660`
1237B{1247C|1257D}1267E~
1277FDEL

Note: This table shows the most commonly used ASCII characters. Standard ASCII uses 7 bits (0-127), while Extended ASCII uses 8 bits (0-255). The table displays key characters including control codes, digits, uppercase and lowercase letters, and common symbols.

Unicode – A Universal Character Set

Developed in 1991 to overcome ASCII limitations. Can store all languages and symbols worldwide. Uses 16-bit or 32-bit codes instead of 7-bit ASCII.

Unicode Goals:
  • ✓ Universal standard for all writing systems
  • ✓ More efficient than ASCII
  • ✓ Fixed encoding (16-bit or 32-bit per character)
  • ✓ Supports private use characters (for unique languages like Chinese, Japanese)
Unicode Character Table (Examples from Different Languages)
DecimalHexadecimalBinary (16-bit)CharacterLanguage/ScriptDescription
6500410000000001000001AEnglish (Latin)Uppercase A
9700610000000001100001aEnglish (Latin)Lowercase a
200134E2D0100111000101101中Chinese (Simplified)Middle/Center
2599165870110010110000111文Chinese (Simplified)Text/Writing
2226956FD0101011011111101国Chinese (Simplified)Country
157506270000011000100111اArabicAlif
157606280000011000101000بArabicBa
158706330000011000110011سArabicSeen
232509150000100100010101कHindi (Devanagari)Ka
2366093E0000100100111110ाHindi (Devanagari)Vowel sign
236009380000100100111000शHindi (Devanagari)Sha
1235430420011000001000010あJapanese (Hiragana)A
1235630440011000001000100いJapanese (Hiragana)I
1235830460011000001000110うJapanese (Hiragana)U
8730221A0010001000011010√MathematicalSquare root
871222080010001000001000∈MathematicalElement of
8747222B0010001000101011∫MathematicalIntegral
96003C00000001111000000πMathematicalPi
836420AC0010000010101100€CurrencyEuro
837720B90010000010111001₹CurrencyIndian Rupee
16500A50000000010100101¥CurrencyYen/Yuan
16300A30000000010100011£CurrencyPound Sterling
1285121F60011111011000000000😀EmojiGrinning face
1285251F60D11111011000001101😍EmojiHeart eyes
1281511F49711111010010010111💗EmojiGrowing heart
1279251F3B511111001110110101🎵EmojiMusical note

Note: Unicode can represent over 1.1 million characters from hundreds of writing systems worldwide. The table above shows examples from different languages and scripts to demonstrate Unicode's universality. Unicode uses 16-bit (UTF-16) or 32-bit (UTF-32) encoding, allowing it to support characters from English, Chinese, Arabic, Hindi, Japanese, and many other languages, as well as mathematical symbols, currency symbols, and emojis.

Unicode supports:

English, French, Chinese, Hindi, Arabic, and more! Mathematical symbols, emojis (😂, ❤️, 🎵), and currency symbols (€, ₹, $).

ASCII vs Unicode Comparison

FeatureASCIIUnicode
Year19631991
Bit Length7-bit (128 chars) or 8-bit (256 chars)16-bit or 32-bit (65,536+ chars)
LanguagesEnglish onlyAll languages
Symbols & EmojisNoYes ✓
Control CharactersYes ✓Yes ✓
Storage EfficiencySmall file sizesLarger file sizes

Note: ASCII is a subset of Unicode. Unicode keeps the first 128 ASCII characters the same to maintain compatibility. Unicode is the modern standard used in web development, databases, and programming.

Explain how the word 'RED' is represented using a character set:
  • • Unique binary/denary number given/stored for each character
  • • The code for R is stored, then the code for E, then D in sequence

Image Representation

What is a Pixel?

A pixel (short for "picture element") is the smallest unit of a digital image or display. Can be Square/Circle.

What is a Bitmap Image?

A bitmap image is made up of small picture elements (pixels) arranged in a two-dimensional grid. Each pixel is represented using binary values.

Pixel Representation in Binary:
  • ✓Black & White Image → 1 bit per pixel (0 = black, 1 = white)
  • ✓2-bit Colour Depth → 4 colours (00, 01, 10, 11)
  • ✓3-bit Colour Depth → 8 colours (000 to 111)
  • ✓8-bit Colour Depth → 256 colours (2⁸ = 256)
  • ✓24-bit Colour Depth → 16.7 million colours (2²⁴ = 16,777,216)

Colour Depth

Colour depth is the number of bits used per pixel to represent different colours.

Formula: Total Colours = 2ⁿ, where n = number of bits per pixel

Colour Depth (bits per pixel)Total Colours
1-bit (Black & White)2
2-bit4
3-bit8
8-bit256
16-bit65,536
24-bit16.7 million
32-bit4.3 billion

Higher colour depth = Better image quality but larger file size.

Image Resolution & Quality

Resolution refers to the number of pixels in an image (width × height).

Higher resolution means more pixels, leading to better quality but larger file size.

ResolutionTotal Pixels
1024 × 768786,432 pixels
1920 × 10802,073,600 pixels
4K (3840 × 2160)8,294,400 pixels

Higher resolution images require more storage.

Effect of Resolution on Image Quality

High Resolution

Sharp and detailed image ✓

Low Resolution

Pixelated and blurry image ✗

Example: A 4K image is much clearer than a 480p image due to more pixels. Lowering resolution reduces file size but decreases image quality.

Image Size Calculation:
Image size = Width × Height × Color depth (bits per pixel)
Example: 1920 × 1080 image with 24-bit color depth
Size = 1920 × 1080 × 24 bits
= 4,976,640 bits
= 622,080 bytes
= ~607 KB

Data Storage Units

Basic Units

  • •Bit: The smallest unit of data in computing, representing a 0 or 1
  • •Nibble: A 4-bit group (half of a byte)
  • •Byte: A group of 8 bits
💡
Memory Aid: "Ko Ma Gi To Pie"

Remember this acronym to help you recall the order of binary units: Ko Ma Gi To Pie

Ko = KiB
Ma = MiB
Gi = GiB
To = TiB
Pie = PiB

The order is very important when doing conversions!

Binary Units (KiB, MiB, GiB)
UnitEquivalent
1 Bit0 or 1
1 Nibble4 Bits
1 Byte8 Bits
1 KiB1024 Bytes
1 MiB1024 KiB
1 GiB1024 MiB
1 TiB1024 GiB
1 PiB1024 TiB
1 EiB1024 PiB

Used by: Computer Memory (RAM)

Decimal Units (KB, MB, GB)
UnitEquivalent
1 KB1,000 Bytes
1 MB1,000 KB
1 GB1,000 MB
1 TB1,000 GB
1 PB1,000 TB
1 EB1,000 PB

Used by: Hard Drive/SSD manufacturers

Note: Storage capacity is measured in both decimal (KB, MB) and binary (KiB, MiB) formats. Kilobyte (KB) = 1000 bytes (decimal), Kibibyte (KiB) = 1024 bytes (binary).

Quick Conversions:
8 bytes = 16 nibbles
512 KiB = 0.5 MiB
4 GiB = 4096 MiB
1 EiB = 1024 PiB

⚠️ Important Note: Please verify and triple-check all calculations to ensure everything is aligned. These calculations are critical for exam success, and accuracy is essential.

File Size Calculations

In this topic, we learn how to calculate the file size required to store bitmap images and sound files. These questions are very common in exams and require careful use of formulas and correct unit conversions.

Bitmap Image File Size

The file size of a bitmap image depends on:

  • Image resolution (number of pixels)
  • Colour depth (bits per pixel)

Formula:

Image size (bits) = total number of pixels × colour depth

Example: Image File Size

An image has a resolution of 800 × 600 pixels and a colour depth of 24 bits. Calculate the file size in MiB.

Step 1: Calculate total number of pixels

800 × 600 = 480,000 pixels

Step 2: Convert to bits

480,000 × 24 = 11,520,000 bits

Step 3: Convert bits to bytes

11,520,000 ÷ 8 = 1,440,000 bytes

Step 4: Convert bytes to MiB

1,440,000 ÷ 1,048,576 ≈ 1.37 MiB

Final Answer: The image file size is approximately 1.37 MiB

✔️ Verified

Sound File Size

The size of a sound file depends on:

  • Sample rate (Hz)
  • Sample resolution (bits)
  • Length of the recording (seconds)
  • Number of channels

Formula for mono sound:

File size (bits) = sample rate × sample resolution × time

For stereo sound, multiply the final result by 2.

Example: Mono Sound File

A mono sound recording has:

  • Sample rate = 22,050 Hz
  • Sample resolution = 16 bits
  • Length = 30 seconds

Calculate the file size in MiB.

Step 1: Calculate size in bits

22,050 × 16 × 30 = 10,584,000 bits

Step 2: Convert bits to bytes

10,584,000 ÷ 8 = 1,323,000 bytes

Step 3: Convert bytes to MiB

1,323,000 ÷ 1,048,576 ≈ 1.26 MiB

Final Answer: The mono sound file size is approximately 1.26 MiB

✔️ Verified

Stereo Sound Note

If the same recording was stereo:

1.26 × 2 = 2.52 MiB

✔️ Verified

📝 Exam Notes
  • •Always divide by 8 when converting bits to bytes
  • •Always use 1024 × 1024 (1,048,576) when converting bytes to MiB
  • •Stereo sound files are double the size of mono
  • •Units must be written clearly at each step

Sound Representation

Key Terms

Sample Rate/Sampling Frequency

Number of audio samples taken per second when converting analog sound wave to digital format. It is measured in Hertz (Hz).

Sample Resolution (Bit Depth)

Number of bits used to represent each audio sample in digital sound recording. Determines accuracy and dynamic range of the recorded sound.

Why recording sound with a higher sampling resolution creates a more accurate recording:
  • • More bits allocated to each amplitude
  • • Amplitudes can be more precise
  • • A wider range of amplitudes can be recorded

One other way to improve accuracy: Increase sample rate

How Sampling is Used to Record a Sound Clip

Sampling is the process of converting an analog sound wave into a digital format that can be stored and processed by a computer.

Steps:
  1. Sound Wave is captured → Microphone converts the analog sound wave into an electrical signal
  2. ADC (Analog to Digital Converter) → The continuous sound wave is measured at regular intervals (samples)
  3. Sampling Rate (Frequency) → The number of samples taken per second measured in Hertz (Hz)
    Example: 44.1 kHz means 44,100 samples per second (CD-Quality)
  4. Quantization → Each sample is assigned a numeric value (Bit Depth) representing the amplitude (loudness) of the sound at that moment
  5. Binary Storage → Sample value is stored as binary data allowing digital playback
Impact of Sampling Rates:
  • • High Sampling Rate → More accurate sound reproduction but larger file size
  • • Higher Bit Depth → More precise amplitude storage, leading to better sound quality
  • • Lower Sampling Rate → Less accurate, e.g., muffled or robotic sound

Common Formats: MP3, WAV, AAC

Sampling

Sound is an analog signal (continuous wave). To store it digitally, we must sample the sound wave at regular intervals and convert each sample to a binary number.

Key Terms:
Sample Rate:
Number of samples taken per second (Hz). Common: 44.1 kHz, 48 kHz
Bit Depth:
Number of bits per sample. Common: 16-bit, 24-bit
File Size Calculation:
Size = Sample Rate × Bit Depth × Duration × Channels
Example Calculation:
3-minute song, 44.1 kHz, 16-bit, stereo (2 channels)
Size = 44,100 × 16 × 180 × 2 bits
= 254,016,000 bits
= 31,752,000 bytes
= ~30.3 MB

Quality vs. File Size: Higher sample rates and bit depths produce better quality but larger files. Compression (MP3, AAC) reduces file size while maintaining acceptable quality.

1.3 Data Storage and File Compression

Metadata

What is Metadata?

Metadata is data about data. It provides information about a file's properties, characteristics, and attributes without being part of the actual content.

Think of metadata as a "label" or "tag" that describes what the file contains, when it was created, who created it, and other relevant information.

Examples of Metadata:

📷Image Metadata

Common image metadata includes:

  • File name: photo.jpg
  • File size: 2.5 MB
  • Dimensions: 1920 × 1080 pixels
  • Resolution: 72 DPI (dots per inch)
  • Color depth: 24-bit (RGB)
  • Date created: 2024-01-15 14:30:25
  • Camera model: Canon EOS 5D
  • Location (GPS): Latitude: 28.6139°N, Longitude: 77.2090°E
  • Author/Photographer: John Doe
🎵Audio/Song Metadata

Common audio metadata (ID3 tags) includes:

  • Title: "Bohemian Rhapsody"
  • Artist: Queen
  • Album: A Night at the Opera
  • Genre: Rock
  • Year: 1975
  • Duration: 5:55 (5 minutes 55 seconds)
  • Bit rate: 320 kbps
  • Sample rate: 44.1 kHz
  • File format: MP3
  • File size: 13.6 MB
🎬Video Metadata

Common video metadata includes:

  • Title: vacation_video.mp4
  • Duration: 00:15:30 (15 minutes 30 seconds)
  • Resolution: 1920 × 1080 (Full HD)
  • Frame rate: 30 fps (frames per second)
  • Video codec: H.264
  • Audio codec: AAC
  • File size: 450 MB
  • Date recorded: 2024-07-20
  • Camera/Device: iPhone 14 Pro
📄Document Metadata

Common document metadata includes:

  • Title: "IGCSE Computer Science Notes"
  • Author: Jane Smith
  • Created date: 2024-01-10
  • Modified date: 2024-01-25
  • Number of pages: 45
  • Word count: 12,500 words
  • File format: PDF
  • File size: 3.2 MB
  • Subject/Tags: Education, Computer Science, IGCSE
Why is Metadata Important?
  • ✓Organization: Helps organize and search for files easily
  • ✓Identification: Provides information about file origin, creator, and purpose
  • ✓Compatibility: Helps software understand how to process the file
  • ✓Copyright: Can include copyright and licensing information
  • ✓Search: Enables better search and filtering of files

Why is Data Compression Needed?

Files such as images, videos, and sound can be very large. Compression helps in:

📝 Exam Keywords

  • ✓Saving storage space (reduces file size on hard drives and cloud storage)
  • ✓Faster streaming (reduces buffering for music/videos)
  • ✓Faster downloads/uploads (less time to transfer files)
  • ✓Reduces network bandwidth usage (less internet data used)
  • ✓Cost-saving (cloud storage and internet service providers charge based on data usage)

Key Point: Compressed files use fewer bits, leading to faster transmission and reduced storage costs.

Types of File Compression

Compression TypeDefinitionKey FeaturesExamples
Lossy CompressionRemoves some data permanentlySmaller file size, cannot recover originalMP3, MP4, JPEG
Lossless CompressionReduces file size without losing any dataCan fully restore original fileRLE, ZIP, PNG

Compression Techniques

Lossless Compression

Original data can be perfectly reconstructed. No information is lost.

  • •Run-Length Encoding (RLE): Replaces repeated sequences with count + value
  • •Dictionary Encoding: Replaces common patterns with shorter codes
  • •Examples: ZIP, PNG, FLAC
  • •Use cases: Text files, program code, medical images

Past Paper Question: How does a lossless algorithm work?

Question: Explain how a lossless compression algorithm works.

Answer (Any three points):

  • •The size of the file is reduced without permanently removing any data.
  • •A compression algorithm is used, such as Run Length Encoding (RLE).
  • •Repeating pixels are identified / Patterns are identified.
  • •These patterns are stored with the number of times they are repeated.
  • •The patterns are indexed for efficient storage and retrieval.

Lossy Compression

Some data is permanently removed. Original cannot be perfectly reconstructed, but file size is significantly reduced.

  • •JPEG: Removes details imperceptible to human eye
  • •MP3: Removes frequencies humans can't hear well
  • •Examples: JPEG, MP3, MPEG video
  • •Use cases: Photos, music, videos (where small quality loss is acceptable)

Lossy Compression Formats

MP3 (MPEG-3) - Lossy Compression for Audio
  • ✓ Reduces audio file size by 90%
  • ✓ Removes frequencies humans can't hear
  • ✓ Uses Perceptual Music Shaping (keeps louder sounds, removes softer ones)
  • ✓ Reduces Bit Depth
Example: A 100MB CD-quality audio file can be reduced to 10MB in MP3 format
MP4 (MPEG-4) - Lossy Compression for Video
  • ✓ Stores multimedia files (video, audio, images, animations)
  • ✓ Smaller file size, retains acceptable quality
  • ✓ Common for online streaming (Netflix, YouTube, etc.)
Example: A 5GB uncompressed video can be reduced to 500MB in MP4 format
JPEG - Lossy Compression for Images
  • ✓ Reduces Colour Depth
  • ✓ Removes small colour details that the human eye doesn't notice
  • ✓ Splits images into 8×8 pixel blocks to discard unnecessary data
  • ✓ Reduces resolution
Example: A 10MB raw image can be reduced to 1MB in JPEG format

JPEG is widely used for online images, as the reduction in quality is often unnoticeable.

Lossless Compression - Run-Length Encoding (RLE)

A specialized algorithm that supports the compression of files by replacing repeated data with a symbol and a count. It's a lossless compression technique.

How RLE Works:
  • ✓ Replaces repeated characters with a count + value
  • ✓ Works best on long runs of repeating data

Limitation: Doesn't work well if no repeating characters are present (e.g., cdcdcdcdcd).

RLE Example 1: Simple Pattern (Black & White Only)
Color Encoding:

For black and white images, we use a simple format:

  • 0 = Black
  • 1 = White

Note: RGB format (Red, Green, Blue values) is only needed for color images. For black and white, we simply use 0 or 1.

8×8 Pixel Grid (Capital Letter F):
RLE Encoding Process:

Reading the grid row by row from left to right, we group consecutive pixels of the same color:

RLE Output (format: count, color) where 0 = black, 1 = white:

8, 0 (Row 1: 8 black pixels)
8, 0 (Row 2: 8 black pixels)
2, 0 (Row 3: 2 black)6, 1 (6 white)
2, 0 (Row 4: 2 black)6, 1 (6 white)
5, 0 (Row 5: 5 black)3, 1 (3 white)
5, 0 (Row 6: 5 black)3, 1 (3 white)
2, 0 (Row 7: 2 black)6, 1 (6 white)
2, 0 (Row 8: 2 black)6, 1 (6 white)

Note: For black and white images, we use a simple format (count, color) where 0 = black and 1 = white. RGB format is only needed for color images.

File Size Calculations:

Uncompressed File Size:

Total pixels = 8 × 8 = 64 pixels
Size = 64 pixels × 1 bit (black/white) = 64 bits = 8 bytes
(Note: For black & white images, we only need 1 bit per pixel: 0 = black, 1 = white)

Compressed File Size (RLE):

Counting runs: Row 1 (1 run) + Row 2 (1 run) + Rows 3-8 (2 runs each) = 14 runs
Each run = 2 values (count, color) × 1 byte = 2 bytes
Size = 14 runs × 2 bytes = 28 bytes

Compression Ratio: 8 bytes ÷ 28 bytes = 1:3.5 (Actually increases size - RLE is less efficient for small, simple images)

Note: RLE works best for images with large areas of the same color. For this small 8×8 image, uncompressed format is actually smaller.

Conclusion:

Important Note about RLE for Small Images:

  • For this small 8×8 image, RLE actually increases the file size (8 bytes → 28 bytes)
  • This happens because storing the count and color values (2 bytes per run) takes more space than the simple 1-bit-per-pixel format
  • RLE works best for larger images with long runs of the same color
  • For very small images, the uncompressed format (1 bit per pixel) is more efficient

Key Takeaway: RLE compression is most effective when images have large areas of uniform color and when the image size is substantial enough that the overhead of storing run-lengths is offset by the compression benefits.

RLE Example 2: Complex Pattern (Black, White & Red)
Color Definitions (RGB Values):
ColorRedGreenBlue
Black000
White255255255
Red25500
8×8 Pixel Grid (Pattern with Colors):
RLE Encoding Process:

Reading the grid row by row from left to right, we group consecutive pixels of the same color:

RLE Output (format: count, red, green, blue):

2, 0, 0, 0 (Row 1: 2 black)2, 255, 0, 0 (2 red)4, 255, 255, 255 (4 white)
2, 0, 0, 0 (Row 2: 2 black)2, 255, 0, 0 (2 red)4, 255, 255, 255 (4 white)
2, 0, 0, 0 (Row 3: 2 black)2, 255, 255, 255 (2 white)2, 255, 0, 0 (2 red)2, 255, 255, 255 (2 white)
2, 0, 0, 0 (Row 4: 2 black)2, 255, 255, 255 (2 white)2, 255, 0, 0 (2 red)2, 255, 255, 255 (2 white)
4, 0, 0, 0 (Row 5: 4 black)2, 255, 255, 255 (2 white)2, 255, 0, 0 (2 red)
4, 0, 0, 0 (Row 6: 4 black)2, 255, 255, 255 (2 white)2, 255, 0, 0 (2 red)
2, 0, 0, 0 (Row 7: 2 black)6, 255, 255, 255 (6 white)
2, 0, 0, 0 (Row 8: 2 black)6, 255, 255, 255 (6 white)
File Size Calculations:

Uncompressed File Size:

Total pixels = 8 × 8 = 64 pixels
Size = 64 pixels × 3 bytes (RGB) = 192 bytes

Compressed File Size (RLE):

Total RLE values = 24 runs (count + RGB values)
Each run = 4 values (count, R, G, B) × 1 byte = 4 bytes
Size = 24 runs × 4 bytes = 96 bytes

Compression Ratio: 192 bytes ÷ 96 bytes = 2:1

Conclusion:

RLE still works for this image, but less efficiently because:

  • The pattern has more color changes (black, white, and red)
  • More runs are needed to represent the same 64 pixels (24 runs)
  • The compression ratio is 2:1
  • RLE works best when there are longer runs of the same color

Note: RLE would work poorly for complex images with many color changes (e.g., photographs), as there would be few repeating sequences to compress.

Describe how lossless compression compresses a text file:
  • • A compression algorithm is used
  • • Such as RLE/run length encoding
  • • Repeating characters are identified / Patterns are identified
  • • And indexed
  • • With number of occurrences
  • • With their position

Comparing Lossy vs. Lossless Compression

FeatureLossy CompressionLossless Compression
File SizeSmallerLarger
Data LossYes (Irreversible)No (Reversible)
Common FormatsMP3, MP4, JPEGRLE, ZIP, PNG
Best forMusic, video, photosDocuments, software, images
Quality Loss?YesNo

Choosing Compression: Need high quality? → Use Lossless RLE. Need smaller files? → Use Lossy (JPEG, MP3, MP4).

Compression Ratio

Compression ratio = Original size ÷ Compressed size

Example: 10 MB file compressed to 2 MB
Compression ratio = 10 ÷ 2 = 5:1

Important: Lossy compression is acceptable for media files but should never be used for text documents, program code, or any data where accuracy is critical.

Chapter Summary

  • Number systems (Binary, Denary, Hexadecimal) are fundamental to computing
  • Character encoding (ASCII, Unicode) allows text representation in binary
  • Images are represented as grids of pixels with color depth determining quality
  • Sound is digitized through sampling at regular intervals
  • Compression reduces file sizes (lossless preserves data, lossy sacrifices some quality)

Related Resources

Practice QuestionsView All Modules
Get in Touch
CodeHaven - Master Computer Science