What is the fundamental difference between a bitmap image and a vector image?

Bitmaps are composed of a fixed grid of pixels where each pixel has a specific color, making them ideal for photos but poor for scaling. Vectors use mathematical equations to define shapes, allowing them to be scaled infinitely without losing any quality.

How does increasing the resolution of an image affect its file size and quality?

Increasing resolution increases the total number of pixels, which improves image detail and sharpness (quality). However, because there are more pixels to store, the file size increases proportionally to the total pixel count.

If you double both the width and the height of a bitmap image, by what factor does the file size increase?

The file size increases by a factor of 4. This is because the total number of pixels is calculated as $Width \times Height$; doubling both dimensions results in $2W \times 2H = 4(W \times H)$.

What is the purpose of metadata in an image file?

Metadata provides 'data about data,' containing essential information like image dimensions and color depth so the computer knows how to display the pixels, as well as descriptive info like GPS location or date taken.

How many colors can be represented by a color depth of 5 bits?

A 5-bit color depth can represent 32 colors. This is calculated using the formula $2^n$, where $n$ is the number of bits ($2^5 = 32$).

What common mistake is made when converting the total number of bits in an image to bytes?

Students often forget to divide the total number of bits by 8. A byte consists of 8 bits, so the formula is $\text{Bytes} = \text{Total Bits} / 8$.

Why is metadata necessary for displaying a bitmap image correctly?

Without metadata like width and height, the computer would just see a long string of binary 0s and 1s. It wouldn't know where one row of pixels ends and the next begins, making it impossible to reconstruct the grid.

Compare 'Resolution' and 'Color Depth' in terms of what they contribute to an image.

Resolution defines the spatial detail (how many points are in the grid), while Color Depth defines the chromatic detail (how many different colors each point can be). Both contribute to quality and file size.

What happens to a bitmap image when it is 'pixelated'?

Pixelation occurs when a low-resolution image is enlarged. The individual pixels become large enough to be visible to the naked eye as distinct squares, causing the image to look blocky and lose its smooth appearance.

If an image requires 100 distinct colors, what is the minimum color depth needed?

The minimum color depth is 7 bits. Since $2^6 = 64$ (too few) and $2^7 = 128$ (enough), 7 bits are required to cover 100 unique colors.

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Representing Images

Summary

Digital images are represented as a grid of discrete elements called pixels, where each pixel's color is encoded as a binary value. The total storage size and visual quality of an image are determined by its resolution (the dimensions of the grid) and its color depth (the number of bits allocated per pixel).

1. Definition & Core Concepts

Bitmap Images: A bitmap is a digital image format composed of a fixed grid of colored squares known as pixels. Unlike vector images which use mathematical paths, bitmaps store specific data for every single point in the image.
The Pixel: Short for 'picture element', a pixel is the smallest individual component of a digital image that can be controlled. Each pixel is assigned a unique binary code that represents its specific color.
Resolution: This refers to the total number of pixels that make up an image, typically expressed as $Width \times Height$ . A higher resolution means more pixels are packed into the same area, resulting in finer detail and a sharper image.

A 5x5 grid representing pixels, with some squares filled with color and containing binary strings to illustrate how color is stored as data.

2. Underlying Principles: Color Depth

3. Methods: Calculating File Size

4. Metadata: Data About Data

Definition: Metadata is additional information stored within an image file that describes the image's properties. While not part of the visual pixel data itself, it is essential for software to correctly interpret and display the file.
Technical Metadata: This includes the image dimensions (width and height), color depth, and file format (e.g., JPEG, PNG). This data tells the computer how to reconstruct the pixel grid on screen.
Descriptive Metadata: This includes contextual information such as the date and time the photo was taken, GPS location coordinates, camera settings (ISO, aperture), and the author's name.

5. Key Distinctions: Bitmap vs. Vector

6. Exam Strategy & Tips