State the formula used to calculate the number of colors available for a given bit depth.

The formula is $Colors = 2^n$, where $n$ represents the bit depth (number of bits per pixel).

How is the total file size of a bitmap estimated in bits?

The file size is estimated by multiplying the image width (in pixels) by the image height (in pixels) and then multiplying that product by the bit depth.

Why does a 24-bit image provide 'True Color'?

It allows for $2^{24}$ (over 16 million) colors, which covers the full range of colors the human eye can typically perceive, allowing for realistic photographic reproduction.

What is the fundamental difference between image resolution and screen resolution?

Image resolution is the total count of pixels within a specific digital file (Width x Height), whereas screen resolution refers to the physical number of pixels available on a display device to show that image.

How does the scalability of a bitmap image compare to that of a vector graphic?

Bitmaps lose quality and become 'pixelated' when scaled up because the fixed grid of pixels is stretched, while vectors use mathematical equations to redraw shapes perfectly at any size.

When should a developer choose a bitmap format over a vector format for a web project?

Bitmaps should be chosen for photographs or images with complex color gradients and textures, whereas vectors are superior for logos and icons that must remain sharp at various sizes.

What is a common error when calculating the file size of a bitmap in bytes?

A frequent mistake is leaving the final answer in bits (Resolution x Bit Depth) without dividing by 8 to convert the value into bytes.

Why is it incorrect to assume that doubling the bit depth will double the number of available colors?

The number of colors is an exponential relationship ($2^n$); therefore, doubling the bit depth (e.g., from 4 to 8) actually squares the number of colors (from 16 to 256).

What happens to the visual quality of an image if you increase the resolution but keep the physical display size the same?

The pixel density (PPI) increases, resulting in a sharper, more detailed image with less visible 'pixelation' to the human eye.

Define 'Color Depth' in the context of bitmap encoding.

Color depth is the specific number of bits allocated to each pixel in an image to store its color information, which determines the total palette size.

Bitmap images | Cambridge International Examinations AS-Level Computer Science

Revision Notes

AS-Level

Cambridge International Examinations

Computer Science

1. Information representation

Bitmap images

Summary

Bitmap images are digital graphics composed of a grid of individual pixels, where each pixel is assigned a specific binary code to represent its color. The quality and storage requirements of these images are fundamentally determined by their resolution and color depth, necessitating a balance between visual fidelity and file size.

1. Definition & Core Concepts

A bitmap image is a data structure representing a rectangular grid of pixels, which are the smallest individual elements of a digital image. Each pixel acts as a tiny square of color that, when viewed together from a distance, forms a cohesive visual representation such as a photograph.

Every pixel in a bitmap is stored as a unique binary code that corresponds to a specific color in the image's color palette. The complexity and variety of colors available in an image are directly tied to the length of these binary strings.

A diagram showing a grid of pixels where one pixel is highlighted and labeled with a binary code, representing how bitmap data is structured.

2. Resolution and Pixel Density

Image resolution is defined as the total number of pixels that constitute a bitmap, typically calculated by multiplying the image width by its height in pixels. Higher resolutions result in finer detail and smoother transitions between colors, but they also increase the amount of data that must be processed and stored.

Pixel Density, measured in Pixels Per Inch (PPI), describes the concentration of pixels within a physical area of a display. To calculate the PPI of a screen, one must use the Pythagorean theorem to find the diagonal resolution in pixels and then divide that value by the physical diagonal size of the screen in inches.

Screen resolution specifically refers to the number of horizontal and vertical pixels a display device can show, such as 1920 x 1080 (1080p). When an image's resolution does not match the screen's density, it may need to be scaled, which can lead to a loss of sharpness or the appearance of a 'pixel grid'.

3. Color Depth and Bit Depth

4. File Size Calculation and Metadata

5. Key Distinctions: Bitmap vs. Vector

Feature	Bitmap Images	Vector Graphics
Composition	Individual pixels (grid)	Mathematical equations and paths
Scalability	Loses quality (pixelates) when enlarged	Infinitely scalable without quality loss
Best Use	Photographs and complex textures	Logos, icons, and typography
File Size	Increases with resolution/depth	Depends on the complexity of shapes

Bitmaps are the preferred format for capturing the real world because they can record subtle variations in light and color that mathematical vectors cannot easily replicate. However, they are less flexible for design work that requires frequent resizing across different media.

6. Exam Strategy & Tips

Bitmap images

Summary

1. Definition & Core Concepts

A diagram showing a grid of pixels where one pixel is highlighted and labeled with a binary code, representing how bitmap data is structured.

2. Resolution and Pixel Density

3. Color Depth and Bit Depth

Color depth, also known as bit depth, refers to the number of bits used to represent the color of a single pixel. This value determines the maximum number of unique colors that can be displayed in an image.

The relationship between bit depth ( $n$ ) and the number of available colors is exponential, expressed by the formula: $Colors = 2^n$ . For example, a 1-bit image can only represent 2 colors (black and white), while an 8-bit image can represent 256 different colors.

True Color typically refers to a 24-bit depth, which allows for over 16 million colors ( $2^{24}$ ). This provides enough variety to represent photographic images with realistic gradients and shadows that are indistinguishable to the human eye.

4. File Size Calculation and Metadata

The estimated file size of a raw bitmap image is calculated by multiplying the total number of pixels (resolution) by the color depth (bits per pixel). The resulting value in bits is usually converted into larger units like bytes, KiB, or MiB for practical use.

Formula: $Size_{bits} = Width \times Height \times Bit\,Depth$

To convert bits to bytes, divide by 8.
To convert bytes to Kibibytes (KiB), divide by 1024.

Every bitmap file includes a file header, which is a block of metadata stored at the beginning of the file. This header contains essential information for the computer to render the image correctly, including the file type (e.g., .bmp, .jpg), the file size, the image resolution, and the bit depth.

5. Key Distinctions: Bitmap vs. Vector

Feature	Bitmap Images	Vector Graphics
Composition	Individual pixels (grid)	Mathematical equations and paths
Scalability	Loses quality (pixelates) when enlarged	Infinitely scalable without quality loss
Best Use	Photographs and complex textures	Logos, icons, and typography
File Size	Increases with resolution/depth	Depends on the complexity of shapes

6. Exam Strategy & Tips

Unit Conversion: Always check if the exam question asks for the file size in bits, bytes, or KiB. Forgetting to divide by 8 to reach bytes is a very common error that results in lost marks.
Color Depth Logic: If a question provides the number of colors needed (e.g., 50 colors), you must find the smallest power of 2 that is greater than or equal to that number (in this case, $2^6 = 64$ , so 6 bits are required).
Header Awareness: Remember that the calculated file size is often an 'estimate' because the actual file will be slightly larger due to the inclusion of the file header and potential compression data.
Scaling Effects: Be prepared to explain why a high-resolution image might still look 'pixelated' on a low-density screen or when zoomed in beyond its native resolution.