Show understanding of how data for a bitmapped image are encoded

Cambridge A‑Level Computer Science 9618 – 1.2 Multimedia & Core Foundations

Learning Objectives

• Explain how data are represented in binary, hexadecimal, BCD and two’s‑complement forms.
• Describe character encodings (ASCII, Unicode) and colour‑depth concepts.
• Identify the main hardware components of a computer system and the role of different memory types.
• Outline the Von Neumann architecture, the fetch‑decode‑execute cycle and the purpose of interrupts.
• Analyse how bitmap and vector images are encoded, calculate their storage requirements and decide which representation is appropriate.
• Understand basic sound sampling, calculate audio file sizes and recognise common audio formats.
• Distinguish between lossless and lossy compression techniques and name the algorithms used in typical multimedia files.

1. Information Representation

1.1 Number Systems

• Binary (base‑2) – digits 0, 1. Used internally by all digital devices.
• Octal (base‑8) – digits 0‑7. Useful for grouping binary in 3‑bit blocks.
• Decimal (base‑10) – digits 0‑9. Human‑friendly.
• Hexadecimal (base‑16) – digits 0‑9, A‑F. Groups binary in 4‑bit nibbles; common in memory addresses.

Quick conversion table (8‑bit values)

1.2 Binary‑Coded Decimal (BCD)

Each decimal digit is stored in a separate 4‑bit nibble. Example: 93₁₀ → 1001 0011₂ (9 = 1001, 3 = 0011). BCD simplifies decimal‑oriented I/O but wastes half the bits compared with pure binary.

1.3 Signed Numbers – Two’s‑Complement

• Range for an n‑bit two’s‑complement integer: –2ⁿ⁻¹ … 2ⁿ⁻¹ – 1.
• Negative value = invert all bits (one’s complement) then add 1.

Example (8‑bit)

+45  → 0010 1101
-45  → invert → 1101 0010, add 1 → 1101 0011 (binary) = –45

1.4 Character Encodings

• ASCII – 7‑bit code (0‑127) covering English letters, digits and control characters.
• Extended ASCII – 8‑bit, adds 128‑255 for additional symbols.
• Unicode (UTF‑8/UTF‑16) – supports > 1 million characters; UTF‑8 is backward compatible with ASCII.

1.5 Colour Depth & Palette

• Colour depth = bits per pixel (bpp). Determines the number of distinct colours: 2^(bpp).
• Palette (indexed colour) stores a table of RGB triples; each pixel holds only an index into that table.

Common colour depths

2. Computer Hardware Fundamentals

2.1 Core Components

• CPU (Central Processing Unit) – executes instructions; contains ALU, registers, control unit.
• Memory hierarchy

  • Registers – fastest, inside CPU, a few bytes each.
  • Cache – SRAM, speeds up access to frequently used data.
  • Main memory (RAM) – volatile; DRAM (dynamic) is common, SRAM is faster but more expensive.
  • Secondary storage – HDD, SSD, optical media; non‑volatile.

• Input/Output (I/O) devices – keyboards, mouse, display, speakers, sensors, actuators.
• Bus system – set of parallel wires that transfer data, addresses and control signals (e.g., system bus, address bus, data bus).

2.2 Memory Types

2.3 Embedded Systems (example)

Microcontroller + sensors + actuators → performs a dedicated task (e.g., temperature controller). Emphasise the limited memory and real‑time constraints.

3. Processor Fundamentals

3.1 Von Neumann Architecture

• Single memory stores both data and program instructions.
• CPU fetches an instruction, decodes it, executes it, then repeats – the Fetch‑Decode‑Execute (FDE) cycle.

Typical FDE cycle (register‑transfer notation)

FETCH:   MAR ← PC          ; address the next instruction
MBR ← MEM[MAR]    ; fetch instruction
IR  ← MBR
PC  ← PC + 1
DECODE:  Decode IR (determine opcode, operands)
EXECUTE: Perform operation (ALU, memory access, I/O)

3.2 Interrupts

• Asynchronous signals that pause the current instruction stream.
• CPU saves the current PC (and sometimes status registers) on a stack, jumps to an interrupt service routine (ISR), then restores state.
• Types: hardware (external device), software (system call), timer‑based.

3.3 Example: Simple addition with an interrupt

; Assume accumulator A holds first operand
INT 0x10          ; hardware interrupt to read second operand into B
ADD B             ; A ← A + B

4. Communication – Networking Fundamentals

4.1 Network Types & Topologies

4.2 Client‑Server vs Peer‑to‑Peer

• Client‑Server – centralised resources (e.g., web server). Scales well for many clients.
• Peer‑to‑Peer – each node can act as client and server (e.g., file‑sharing).

4.3 IP Addressing

• IPv4: 32‑bit dotted‑decimal (e.g., 192.168.1.25). Supports ~4.3 billion addresses.
• IPv6: 128‑bit hexadecimal groups (e.g., 2001:0db8:85a3::8a2e:0370:7334).
• Subnet mask determines network vs host portion; common masks: /24 (255.255.255.0), /16 (255.255.0.0).

Quick subnet example

Network: 192.168.10.0/24
Valid hosts: 192.168.10.1 – 192.168.10.254
Broadcast: 192.168.10.255

4.4 Core Protocols

• TCP – connection‑oriented, reliable, ordered delivery.
• UDP – connectionless, low‑latency, no guarantee of delivery.
• HTTP / HTTPS – application‑layer protocol for web traffic.
• DNS – translates domain names to IP addresses.
• Ethernet / Wi‑Fi – physical and data‑link layer technologies; CSMA‑CD (wired) and CSMA‑CA (wireless) for media access.

4.5 Example Exam Question (AS)

Given the IPv4 address 172.16.5.130/20, determine the network address and the range of usable host addresses.

Solution

/20 → subnet mask 255.255.240.0
Network address: 172.16.0.0
First host:      172.16.0.1
Last host:       172.16.15.254
Broadcast:       172.16.15.255

5. Multimedia – Bitmap (Raster) Images – Encoding

5.1 Key Concepts

• Pixel – smallest addressable element; identified by (x, y) coordinates.
• Resolution – width × height in pixels.
• Colour depth – bits per pixel (bpp).
• Palette (colour table) – used in indexed‑colour images.
• Bit planes – all bits occupying the same position across pixels; useful for image‑processing.

5.2 Colour‑Encoding Methods

Direct (True‑colour) Encoding

• Each pixel stores its colour directly, usually as three separate channels R, G, B.
• 24‑bit colour = 8 bits per channel → 16 777 216 possible colours.
• 32‑bit colour adds an 8‑bit alpha channel for transparency.

Indexed (Palette‑based) Encoding

• Pixel stores an index (1, 2, 4 or 8 bits) into a palette that holds the actual RGB triples.
• Reduces file size when the image uses a limited set of colours.

5.3 Calculating Bitmap Data Size

Raw size (bits)

\[

\text{bits} = \text{width} \times \text{height} \times \text{bpp}

\]

Convert to bytes (divide by 8) and round up to the nearest whole byte. Many file formats pad each scanline to a 4‑byte boundary – add the padding when required.

Worked Example – 640 × 480, 8‑bpp indexed

1. Total pixels = 640 × 480 = 307 200
2. Bits = 307 200 × 8 = 2 457 600 bits
3. Bytes = 2 457 600 ÷ 8 = 307 200 bytes ≈ 300 KB

5.4 Effect of Changing Resolution or Colour Depth

5.5 Data Layout in Memory (row‑major order)

24‑bit RGB (no padding)

Byte 0: Red   of pixel (0,0)
Byte 1: Green of pixel (0,0)
Byte 2: Blue  of pixel (0,0)
Byte 3: Red   of pixel (1,0)
...

8‑bit indexed (no padding)

Byte 0: Palette index of pixel (0,0)
Byte 1: Palette index of pixel (1,0)
...

5.6 Common File Formats & Their Encoding

• BMP – uncompressed RGB or indexed data; optional RLE for 4/8‑bpp.
• GIF – 8‑bpp indexed; uses LZW lossless compression.
• PNG – supports 1‑32 bpp; uses DEFLATE (LZ77 + Huffman) lossless compression.
• JPEG – 24‑bit true‑colour; lossy DCT‑based compression (outside raw bitmap encoding but essential for multimedia).

6. Multimedia – Vector Graphics – Encoding

6.1 What Is a Vector Graphic?

A vector image stores drawing instructions (geometric primitives) rather than colour for every pixel. The file contains coordinates, shapes and styling attributes, making the image resolution‑independent.

6.2 Core Elements

• Objects – line, rectangle, circle, ellipse, polygon, Bézier path.
• Properties – stroke colour, fill colour, line width, opacity, dash pattern.
• Coordinate system – usually a Cartesian grid measured in user units (pixels, points, mm).

Simple SVG Example

<svg width="200" height="100">
<line x1="10" y1="10" x2="190" y2="10"
stroke="blue" stroke-width="2"/>
<circle cx="100" cy="60" r="40" fill="red"/>
</svg>

6.3 File‑Size Considerations

• Size grows with the number of objects and the length of attribute strings, not with image dimensions.
• Very complex drawings (thousands of paths) can become larger than a low‑resolution bitmap.

6.4 When to Use Vector vs. Bitmap

7. Sound – Basic Encoding

7.1 Fundamental Terms

• Sampling rate (frequency) – samples per second (Hz). Common rates: 44.1 kHz (CD), 48 kHz (DVD), 22.05 kHz (telephone).
• Bit depth – bits per sample; defines dynamic range (e.g., 16‑bit → 96 dB).
• Channels – mono (1) or stereo (2); more channels increase size linearly.
• Pulse‑Code Modulation (PCM) – raw, uncompressed audio representation.

7.2 Calculating Audio File Size (PCM)

\[

\text{bits} = \text{duration (s)} \times \text{sampling rate (samples/s)} \times \text{bit depth} \times \text{channels}

\]

Convert to bytes by dividing by 8.

Example – 10 s of CD‑quality audio

1. Samples per channel = 44 100 × 10 = 441 000
2. Total bits = 441 000 × 16 × 2 = 14 112 000 bits
3. Bytes = 14 112 000 ÷ 8 = 1 764 000 bytes ≈ 1.68 MB

7.3 Common Audio Formats

• WAV – stores raw PCM; large, no compression.
• MP3 – lossy, psychoacoustic model; typical reduction to 1 %–10 % of original size.
• AAC / OGG – modern lossy formats with better quality at similar bitrates.
• FLAC – lossless compression; roughly 50 % size reduction while preserving original data.

8. Compression – Overview

8.1 Lossless vs. Lossy

• Lossless – original data can be perfectly reconstructed (PNG, GIF, FLAC, ZIP). Ideal when any degradation is unacceptable.
• Lossy – some information is permanently discarded to achieve higher compression (JPEG, MP3, AAC). Acceptable when a small loss in quality is tolerable for a large size reduction.

8.2 Typical Algorithms Used in Multimedia

8.3 Example Exam Question (A‑Level)

Explain why a PNG image of a line drawing is usually smaller than a JPEG of the same picture, even though both have the same pixel dimensions.

Key points for answer

• PNG uses lossless DEFLATE; JPEG uses lossy DCT which introduces artefacts.
• Line drawings contain large uniform areas → RLE/DEFLATE compresses very well.
• JPEG’s block‑based DCT is inefficient for sharp edges; it creates high‑frequency coefficients that increase size.

9. Choosing the Right Representation – Summary Table

10. Exam‑Style Tips

• Memorise the colour‑depth table and be able to convert bpp → number of colours.
• Practice quick calculations of image and audio file sizes using the provided formulas.
• Know the key differences between lossless and lossy compression; be ready to cite an example of each.
• For networking, be comfortable converting between dotted‑decimal IPv4 and binary, and identifying network/host ranges.
• When asked to choose a representation, reference at least two criteria (e.g., scalability and file size).