Write the expression to find the number of bits to store a digital image
To find the number of bits required to store a digital image, you can use the following expression:
Total number of bits=Width×Height×Bit depth\text{Total number of bits} = \text{Width} \times \text{Height} \times \text{Bit depth}Total number of bits=Width×Height×Bit depth
Where:
- Width: Width of the image in pixels.
- Height: Height of the image in pixels.
- Bit depth: Number of bits used to represent each pixel.
Explanation:
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Width and Height: These represent the dimensions of the image in pixels. For example, a 256 x 256 image has a width of 256 pixels and a height of 256 pixels.
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Bit Depth: This specifies the number of bits used to represent each pixel. It determines the range and precision of colors or gray levels that can be represented. For instance, common bit depths are 8 bits (256 levels), 16 bits (65,536 levels), or 24 bits (16.7 million colors in RGB).
Example:
Let's say you have an image with the following specifications:
- Width = 512 pixels
- Height = 512 pixels
- Bit depth = 24 bits per pixel (true color)
The calculation would be: Total number of bits=512×512×24\text{Total number of bits} = 512 \times 512 \times 24Total number of bits=512×512×24
Total number of bits=8,388,608 bits\text{Total number of bits} = 8,388,608 \text{ bits}Total number of bits=8,388,608 bits
This means you would need 8,388,608 bits (or approximately 1 megabyte) of storage to store this image.
Notes:
- Bit Depth Consideration: The choice of bit depth depends on the required color fidelity and storage constraints. Higher bit depths provide more colors or shades of gray but require more storage space.
- Compression: In practice, digital images are often compressed to reduce storage requirements while maintaining acceptable image quality.
- Units: The result is typically in bits, but for practical purposes, it's often converted to bytes (divide by 8) or megabytes (divide by 8×1068 \times 10^68×106) for easier understanding of storage requirements.
This expression gives a straightforward way to estimate the storage needs for digital images based on their dimensions and bit depth.
