Data Storage and Compression

Objective

Calculate the file size of an image file and a sound file, using information given.

Calculating File Size

File size is the amount of storage space a file occupies on a storage device. It is typically measured in bytes, kilobytes (KB), megabytes (MB), gigabytes (GB), and terabytes (TB).

To calculate file size, we often need information such as the file's bit rate (for audio) or resolution and color depth (for images).

Image File Size Calculation

The size of an image file depends on several factors, including:

• Resolution: The number of pixels in the image (width x height).
• Color Depth: The number of bits used to represent each pixel. Common color depths are 8-bit, 24-bit, and 32-bit.
• Image Format: Different image formats (e.g., JPEG, PNG, GIF) use different compression techniques, which affect file size.

A simplified formula for estimating image file size is:

$$ \text{File Size (bytes)} \approx \frac{\text{Resolution (pixels)} \times \text{Color Depth (bits)} \times \text{Compression Factor}}{8} $$

The compression factor depends on the image format. For example, a JPEG image will have a smaller file size than a PNG image with the same resolution and color depth.

Sound File Size Calculation

The size of a sound file depends on:

• Bit Rate: The number of bits used to represent each second of audio. Common bit rates are 8 kbps, 16 kbps, 32 kbps, and 128 kbps.
• Duration: The length of the sound file in seconds.
• Number of Channels: The number of audio channels (e.g., mono or stereo).

A simplified formula for estimating sound file size is:

$$ \text{File Size (bytes)} \approx \text{Bit Rate (bits/second)} \times \text{Duration (seconds)} \times \frac{\text{Number of Channels}}{8} $$

The number of channels is divided by 8 because each channel typically requires 8 bits.

Example Calculations

Image File Size Example

Consider an image with a resolution of 1000 pixels wide by 800 pixels high, a color depth of 24 bits per pixel (which is 3 bytes per pixel), and it is saved as a JPEG file with a compression factor of 0.5.

Parameter	Value
Resolution (pixels)	1000 x 800
Color Depth (bits/pixel)	24 bits
Compression Factor	0.5

Calculating the file size:

$$ \text{File Size} \approx \frac{1000 \times 800 \times 24 \times 0.5}{8} = \frac{9600000}{8} = 1200000 \text{ bytes} $$

This is equal to 1,200,000 bytes, or 1.2 MB.

Sound File Size Example

Consider a sound file with a bit rate of 128 kbps, a duration of 30 seconds, and 2 audio channels (stereo).

Parameter	Value
Bit Rate (bits/second)	128 kbps = 128,000 bps
Duration (seconds)	30 seconds
Number of Channels	2

Calculating the file size:

$$ \text{File Size} \approx 128000 \times 30 \times \frac{2}{8} = 3840000 \times \frac{1}{4} = 960000 \text{ bytes} $$

This is equal to 960,000 bytes, or 0.96 MB.