Chapter 1.2 - Multimedia

Cambridge 9618 AS Computer Science

📚 Learning Objectives

Understand how data for a bitmapped image are encoded
Perform calculations to estimate file size for a bitmap image
Understand effects of changing elements of a bitmap image
Understand how data for a vector graphic are encoded
Justify use of bitmap image or vector graphic for a given task
Understand how sound is represented and encoded
Understand impact of changing sampling rate and resolution

1.1 Introduction to Graphics

Images are an important type of data that computers handle. To process and display images, computers must represent them in a digital form using binary numbers.

Images can be stored in a computer in two common formats:

🌟 Did You Know?

The word "pixel" is a combination of "picture" and "element". It was first used in 1965 by Frederic C. Billingsley at NASA's Jet Propulsion Laboratory!

1.2 Bitmap Images

📖 Definition: Bitmap Image

A bitmap image is made up of pixels (picture elements). The image is stored in a two-dimensional matrix of pixels. Each pixel can be a small rectangle, a small circle, or a dot.

📖 Definition: Pixel

A pixel is the smallest identifiable component of a bitmap image, defined by just two properties:

Its position in the bitmap matrix
Its colour

Bitmaps are also known as pixelmaps or raster graphics.

How Bitmap Images Work

💡 Exam Tip

When asked about bitmap images in exams, always mention that they are made up of pixels and each pixel has a defined position and colour. This is the key distinction from vector graphics!

1.3 Colour Depth & Bit Depth

📖 Definition: Colour Depth

Colour depth is the number of bits used to represent the colour of each pixel. It determines how many different colours can be displayed.

📖 Definition: Bit Depth

Bit depth is the number of bits used to store each of the red, green, and blue primary colours in an RGB colour model.

The simplest scheme uses 1 bit per pixel (black or white). More bits allow more colours:

Colour/Bit Depth	Number of Colours	Example Use
1 bit	2¹ = 2	Black & White
4 bits	2⁴ = 16	Simple graphics
8 bits	2⁸ = 256	GIFs, retro games
16 bits	2¹⁶ = 65,536	High colour
24 bits (True Colour)	2²⁴ = 16,777,216	High-quality images
32 bits	2³² = 4,294,967,296	Professional graphics

Formula: Number of Colours = 2ⁿ where n = colour depth (bits per pixel)

⚠️ Common Mistake

Don't confuse colour depth with bit depth!

Colour depth = total bits per pixel (e.g., 24 bits for True Colour)
Bit depth = bits per RGB channel (e.g., 8 bits for each of R, G, B)

So 8-bit depth × 3 channels = 24-bit colour depth

🌟 Did You Know?

If a lower bit depth is used, images will show bands of colour instead of smooth gradients. This is called "banding" or "posterization".

1.4 Image Resolution & Screen Resolution

📖 Definition: Image Resolution

Image resolution is the number of pixels in a bitmap file, defined as the product of width and height values.

Example: An image with 1920 × 1080 pixels has 2,073,600 total pixels.

📖 Definition: Screen Resolution

Screen resolution is the product of width and height values for the number of pixels that a screen can display.

Example: A 4K display has 3840 × 2160 pixels.

📖 Definition: Pixel Density

Pixel density is the number of pixels per square inch (PPI - Pixels Per Inch). Higher PPI means sharper display.

Calculating Pixel Density (PPI)

Example: Calculate pixel density for an iPhone 8 with 5.5-inch screen and resolution 1920 × 1080:

Add squares of resolution: (1920)² + (1080)² = 3,686,400 + 1,166,400 = 4,852,800
Find square root: √4,852,800 = 2202.907
Divide by screen size: 2202.907 ÷ 5.5 = 401 PPI

💡 Exam Tip

When image resolution is higher than screen resolution, the image must be either:

Scaled down (removing pixels, may lose quality)
Cropped (showing only part of the image)
Displayed at full size (user must scroll to see all)

⚠️ Important

Why does bitmap image quality become poor during zooming?

When zooming in on a bitmap, the number of pixels stays the same but each pixel is stretched to cover a larger area. This causes the image to look blocky and pixelated.

1.5 Calculating Bitmap File Size

File Size (bits) = Resolution × Colour Depth

File Size (bits) = Width × Height × Bits per Pixel

Worked Example 1

Question: A bitmap graphic fills a laptop screen with resolution 1366 × 768 pixels. Colour depth is 24 bits. Calculate the file size in MiB.

Solution:

Total pixels = 1366 × 768 = 1,049,088 pixels
Total bits = 1,049,088 × 24 = 25,178,112 bits
Bytes = 25,178,112 ÷ 8 = 3,147,264 bytes
KiB = 3,147,264 ÷ 1024 = 3,073.5 KiB
MiB = 3,073.5 ÷ 1024 ≈ 3 MiB

Worked Example 2

Question: Calculate the file size of a bitmap to be printed at 72 dpi, dimensions 5" × 3", with bit depth of 8.

Solution:

Bit depth 8 means 8 bits for each RGB channel = 24 bits total per pixel
Pixels per row = 5 × 72 = 360 pixels
Pixels per column = 3 × 72 = 216 pixels
Total pixels = 360 × 216 = 77,760 pixels
File size = 77,760 × 3 bytes = 233,280 bytes ≈ 228 KiB

📖 Definition: Bitmap File Header

A file header is a set of bytes at the beginning of a bitmap file which identifies the file type and contains metadata about the image.

File header contains:

File type (.bmp, .jpg, etc.)
File size
Image resolution (width × height)
Colour depth / bit depth
Compression type used

⚠️ Common Mistake

Remember: The bitmap file size is larger than the size of just the graphic data because it also includes the file header!

1.6 Vector Graphics

📖 Definition: Vector Graphic

A vector graphic is an image made up of mathematical shapes such as straight lines and curves, using coordinates and geometry to precisely define the parts of the image.

Vector graphics can be designed using:

Computer Aided Design (CAD) software
Drawing applications with a drawing canvas

Key Components of Vector Graphics

🧠 Memory Trick

"V-P-S-C" for Vector Graphics advantages:

Very scalable (no quality loss when resized)
Precise (mathematical definitions)
Small file size
Crisp at any size

Example Drawing List Entry:

Line: Start(10,20), End(50,20), Colour(Black), Thickness(2)
Circle: Centre(100,100), Radius(30), Fill(Red), Border(Black)
Rectangle: Start(200,50), Width(50), Height(30), Border(Blue)

💡 Exam Tip

When a vector graphic is displayed, the file is read and calculations are made to draw the objects. If the user resizes the image, the file is read again and new calculations are made - this is why quality is preserved!

1.7 Bitmap vs Vector Graphics

Feature	Bitmap Images	Vector Graphics
Composition	Made of tiny pixels	Made of mathematical shapes
Scalability	Loses quality when resized (pixelates)	Can be resized infinitely without quality loss
File Size	Large (depends on resolution)	Smaller (uses formulas, not pixels)
Best For	Photographs, complex textures	Logos, icons, diagrams
Editing	Edit individual pixels	Edit shapes and properties
Realism	Very realistic	Less realistic (cartoon-like)
File Formats	.jpg, .png, .bmp, .gif	.svg, .ai, .eps, .cgm, .odg

When to Use Bitmap Images

Photographs: Digital photos where every pixel contains colour information
Complex Art & Textures: Images with shading, gradients, and textures
Realistic Images: Real-world scenes captured by cameras
Web Images: When inserting images into documents or web pages

When to Use Vector Graphics

Logos: Must be resized for different purposes (business cards to billboards)
Icons: Need to appear sharp at different sizes (apps, websites)
Diagrams & Illustrations: Flowcharts, maps, technical drawings
Text-Based Designs: To ensure clarity at any size
Architectural/Engineering Designs: CAD drawings that need precise scaling

🌟 Did You Know?

Vector graphic files can only be displayed directly on a graph plotter. For most displays, they must be converted to bitmap first. This is called rasterisation.

2.1 Sound Representation

📖 Key Concepts

Sound cannot travel in a vacuum - it requires a medium. It is transmitted by causing oscillations of particles within the medium.

The human ear picks up these oscillations (changes in air pressure) and interprets them as sound.

📖 Definition: Analogue vs Digital

Analogue data is data obtained by measurement of a physical property which can have any value from a continuous range of values.

Digital data is data that has been stored as a binary value which can have one of a discrete range of values.

How Sound is Encoded

📖 Definition: Sampling

Sampling is the process of taking measurements at regular intervals and storing the value. Each sample records the amplitude of the sound wave at that point in time.

💡 Exam Tip

Remember the two components of a sound encoder:

Band-limiting filter - removes very high frequencies that human ear cannot detect (would cause coding problems)
ADC (Analogue-to-Digital Converter) - converts analogue data to digital binary values

2.2 Sampling Rate & Sampling Resolution

📖 Definition: Sampling Rate

Sampling rate is the number of samples taken per second, measured in Hertz (Hz).

Example: 44.1 kHz (CD quality) = 44,100 samples per second

📖 Definition: Sampling Resolution

Sampling resolution (also called bit depth) is the number of bits used to store each sample's amplitude.

Example: 16-bit resolution allows 2¹⁶ = 65,536 possible amplitude values

twice the highest frequency in the sound Human hearing: up to 20,000 Hz CD sampling rate: 44,100 Hz (> 2 × 20,000)

Sound File Size (bits) = Sampling Rate × Sampling Resolution × Duration × Channels

Channels: Mono = 1, Stereo = 2

Worked Example

Question: Audio is sampled at 44.1 kHz using 8 bits. Two channels (stereo) are used. Calculate the size of a 30-second recording in MiB.

Solution:

File size = 44,100 × 8 × 30 × 2 = 21,168,000 bits
Bytes = 21,168,000 ÷ 8 = 2,646,000 bytes
MiB = 2,646,000 ÷ (1024 × 1024) ≈ 2.5 MiB

Factor	Effect on Quality	Effect on File Size
Higher Sampling Rate	More detail, better sound quality	Larger file size
Higher Resolution	More precise amplitude, less distortion	Larger file size

⚠️ Common Mistake

Don't forget to account for stereo recordings (2 channels) when calculating file size! Many students forget to multiply by 2.

Key Takeaways

📝 Bitmap Images - Complete Summary

Bitmaps are made up of pixels arranged in a 2D matrix
Each pixel has a defined position (row, column) and colour value
Colour depth = total bits per pixel; determines number of possible colours (2ⁿ)
Bit depth = bits per RGB channel; 8-bit depth × 3 = 24-bit colour depth
Image resolution = number of pixels in the image (width × height)
Screen resolution = pixels the display can show
Pixel density (PPI) = pixels per inch; higher = sharper display
File size formula: Resolution × Colour Depth (then convert units: bits→bytes→KiB→MiB)
Bitmaps lose quality when scaled up (pixelation/blocky appearance)
File header contains metadata: file type, size, resolution, colour depth, compression type
Common formats: .jpg, .png, .bmp, .gif, .tif
Best for: photographs, realistic images, complex textures

📝 Vector Graphics - Complete Summary

Vector graphics use mathematical formulas to define shapes
Store drawing list with commands, attributes, and relative positions
Objects include: lines, circles, rectangles, curves (Bezier), polygons
Dimensions NOT fixed - only relative positions stored
Can be scaled infinitely without any quality loss
Generally have smaller file sizes than bitmaps for simple graphics
When displayed: calculations are made to draw objects; resizing = new calculations
Must be rasterised (converted to bitmap) for most displays
File formats: .svg, .ai, .eps, .cgm, .odg
Best for: logos, icons, diagrams, technical drawings, CAD, text-based designs

📝 Sound Representation - Complete Summary

Sound is analogue; must be converted to digital for computers
Sampling = taking amplitude measurements at regular intervals
Sampling rate = samples per second (Hz); CD uses 44.1 kHz
Sampling resolution = bits per sample; CD uses 16-bit
Nyquist's Theorem: sample rate must be ≥ 2 × highest frequency in sound
Human hearing range: ~20 Hz to 20,000 Hz
Higher sampling rate/resolution = better quality but larger file size
Sound file size: Rate × Resolution × Duration × Channels
Sound encoder components: band-limiting filter + ADC
Amplitude = loudness; Frequency = pitch
Quantisation error = difference between actual and recorded amplitude
Common formats: .wav, .mp3, .aac, .flac, .ogg

🧠 Quick Memory Aid - File Size Formulas

🖼️ Image: W × H × Colour Depth → bits → ÷8 (bytes) → ÷1024 (KiB) → ÷1024 (MiB)

🔊 Sound: Rate × Resolution × Duration × Channels → bits → ÷8 (bytes) → ÷1024 (KiB) → ÷1024 (MiB)

Remember: 1 KiB = 1024 bytes, 1 MiB = 1024 KiB, 1 GiB = 1024 MiB

Or for decimal: 1 KB = 1000 bytes, 1 MB = 1,000,000 bytes

Exam-Style Questions

Q1. A photograph has a bit depth of 8 and image resolution of 1500 pixels wide and 3000 pixels high. Calculate the file size of the photograph in megabytes (MB). [3 marks]

Mark Scheme:

Bit depth of 8 means 8 bits for each RGB channel → 24 bits per pixel (colour depth) ✓
Total pixels = 1500 × 3000 = 4,500,000 pixels ✓
File size = 4,500,000 × 24 = 108,000,000 bits ✓
Convert to bytes: 108,000,000 ÷ 8 = 13,500,000 bytes
Convert to MB: 13,500,000 ÷ 1,000,000 = 13.5 MB ✓

Additional points: If using MiB (1024-based), answer would be ~12.9 MiB. Always check if question asks for MB or MiB.

Q2. Describe how sound is represented in a computer. [4 marks]

Mark Scheme:

Sound is analogue and must be converted to digital ✓
Amplitude is recorded/sampled at set intervals ✓
Each amplitude value is converted to a binary number ✓
Binary values are stored in sequence ✓
Higher sampling rate = more samples per second = better quality
Higher resolution = more bits per sample = more accurate amplitude
Analogue-to-Digital Converter (ADC) used for conversion

Q3. A camera detector has an array of 1920 by 1536 pixels. Colour depth of 16 bits is used. Calculate the size of the photograph, giving your answer in MiB. [3 marks]

Mark Scheme:

Total pixels = 1920 × 1536 = 2,949,120 pixels ✓
Total bits = 2,949,120 × 16 = 47,185,920 bits ✓
Bytes = 47,185,920 ÷ 8 = 5,898,240 bytes
MiB = 5,898,240 ÷ (1024 × 1024) = 5.625 MiB ✓

Q4. Photographs have been taken by a smartphone which uses a detector with a 1024 × 1536 pixel array. Software uses a colour depth of 24 bits. How many photographs could be stored on a 16 GiB memory card? [4 marks]

Mark Scheme:

Total pixels = 1024 × 1536 = 1,572,864 pixels ✓
File size per photo = 1,572,864 × 24 = 37,748,736 bits ✓
Convert to bytes: 37,748,736 ÷ 8 = 4,718,592 bytes ✓
16 GiB = 16 × 1024 × 1024 × 1024 = 17,179,869,184 bytes
Number of photos = 17,179,869,184 ÷ 4,718,592 ≈ 3,640 photos ✓

Note: Real-world answer would be less due to file headers, metadata, and file system overhead.

Q5. Explain the difference between a bitmap image and a vector graphic. Give one example of when each would be the best choice. [5 marks]

Mark Scheme:

Bitmap: Made up of pixels arranged in a grid/matrix ✓
Each pixel has defined position and colour ✓
Loses quality when scaled up (pixelates) ✓
Vector: Made up of mathematical shapes/formulas ✓
Stores drawing list with commands and properties ✓
Can be scaled infinitely without quality loss ✓
Bitmap best for: Photographs, complex textures, realistic images ✓
Vector best for: Logos, icons, diagrams, technical drawings ✓

Q6. A company needs to create a logo that will be used on both business cards and billboards. Justify whether they should use a bitmap or vector graphic. [4 marks]

Mark Scheme:

Should use a vector graphic ✓
Logo needs to be displayed at very different sizes (small card, large billboard) ✓
Vector graphics can be scaled infinitely without quality loss ✓
Bitmap would pixelate/become blurry when enlarged for billboard ✓
Vector files are typically smaller for simple logo designs ✓
Vector allows easy editing of colours and shapes ✓

Exam-Style Questions (continued)

Q7. Audio is being sampled at the rate of 44.1 kHz using 16 bits. Two channels (stereo) are being used. Calculate the size of a 30-second audio recording in MiB. [4 marks]

Mark Scheme:

File size = Sampling Rate × Resolution × Duration × Channels ✓
= 44,100 × 16 × 30 × 2 = 42,336,000 bits ✓
Bytes = 42,336,000 ÷ 8 = 5,292,000 bytes ✓
MiB = 5,292,000 ÷ (1024 × 1024) ≈ 5.05 MiB ✓

Common mistake: Forgetting to multiply by 2 for stereo channels!

Q8. Explain why a bitmap file size is larger than the size of the graphic data alone. [2 marks]

Mark Scheme:

Bitmap file contains file header in addition to pixel data ✓
Header contains metadata: file type, size, resolution, colour depth, compression type ✓
This additional data increases total file size beyond just the graphic data

Q9. What is meant by the term "sampling resolution" when referring to sound files? Explain how increasing the sampling resolution affects the quality and file size of a sound recording. [4 marks]

Mark Scheme:

Definition: Sampling resolution is the number of bits used to store each sample/amplitude value ✓
Effect on quality: Higher resolution = more possible amplitude values = more accurate representation = less distortion/quantisation error ✓
Effect on file size: Higher resolution = more bits per sample = larger file size ✓
Example: 8-bit = 256 values, 16-bit = 65,536 values ✓

Q10. State Nyquist's theorem and explain why it is important when recording sound. [3 marks]

Mark Scheme:

Nyquist's theorem: Sampling rate must be at least twice the highest frequency in the sound being sampled ✓
Importance: Ensures all frequencies in the sound are captured accurately ✓
If sampling rate is too low, high frequencies are lost or cause aliasing (distortion) ✓
Human hearing range: ~20 Hz to 20,000 Hz → CD uses 44,100 Hz (more than 2× 20,000)

Q11. An image has resolution 100 × 200 pixels and colour depth of 8 bits. Calculate its file size in bytes. [2 marks]

Mark Scheme:

Total pixels = 100 × 200 = 20,000 pixels ✓
File size = 20,000 × 8 bits = 160,000 bits = 20,000 bytes ✓

Q12. Describe two advantages and two disadvantages of using bitmap images compared to vector graphics. [4 marks]

Mark Scheme:

Advantages of Bitmap:

Can represent realistic images (photographs) with fine detail ✓
Supports wide range of colours and gradients ✓
Compatible with most devices and software ✓

Disadvantages of Bitmap:

Loses quality when scaled up (pixelates) ✓
Larger file sizes for high resolution images ✓
Cannot easily edit individual components ✓

💡 Exam Success Tips

💡 Tip 1: Unit Conversions

Always check which units the question asks for:

MB = Megabytes (÷ 1,000,000)
MiB = Mebibytes (÷ 1024 × 1024)

Using the wrong conversion will lose marks!

💡 Tip 2: Show Your Working

Always show each step of calculations:

Calculate total pixels/Total bits
Convert to bytes (÷ 8)
Convert to final unit (÷ 1024 for KiB/MiB or ÷ 1000 for KB/MB)

Even if you make an arithmetic error, method marks may be awarded!

💡 Tip 3: Remember Stereo!

For sound calculations involving stereo recordings, always multiply by 2 channels. This is one of the most common mistakes!

💡 Tip 4: Keywords Matter

Use correct terminology in your answers:

Bitmap: pixels, grid, matrix, colour depth
Vector: mathematical, shapes, drawing list, scalable
Sound: sampling, amplitude, ADC, resolution

🧠 Final Memory Check

File Size Formulas:

🖼️ Image: W × H × Depth → bits → bytes → larger units

🔊 Sound: Rate × Resolution × Time × Channels → bits → bytes → larger units

Key Definitions:

• Colour depth = bits per pixel | Bit depth = bits per RGB channel

• Sampling rate = samples/second | Sampling resolution = bits per sample

Nyquist's Theorem: Sample rate ≥ 2 × highest frequency