Data Storage

Data storage is measured in a variety of units, each representing a different size of storage capacity. The smallest unit of measurement is the bit, which represents a single binary digit (either 0 or 1)
A nibble is a group of 4 bits, while a byte is a group of 8 bits
Kibibyte (KiB), mebibyte (MiB), gibibyte (GiB), tebibyte (TiB), pebibyte (PiB), and exbibyte (EiB) are all larger units of measurement
Specifically, 1 KiB is equal to 2¹⁰ bytes, 1 MiB is equal to 2²⁰ bytes, 1 GiB is equal to 2³⁰ bytes, 1 TiB is equal to 2⁴⁰ bytes, 1 PiB is equal to 2⁵⁰ bytes, and 1 EiB is equal to 2⁶⁰ bytes

To calculate the file size of an image file:

Determine the resolution of the image in pixels (width x height)
Determine the colour depth in bits (e.g. 8 bits for 256 colours)
Multiply the number of pixels by the colour depth to get the total number of bits
Divide the total number of bits by 8 to get the file size in bytes
If necessary, convert to larger units like kibibytes, mebibytes, etc

An image measures 100 by 80 pixels and has 128 colours (so this must use 7 bits)

100 x 80 x 7 = 56000 bits ÷ 8 = 7000 bytes ÷ 1024 = 6.84 kibibytes

To calculate the file size of a sound file:

Determine the sample rate in Hz (e.g. 44,100 Hz)
Determine the sample resolution in bits (e.g. 16 bits)
Determine the length of the track in seconds
Multiply the sample rate by the sample resolution to get the number of bits per second
Multiply the number of bits per second by the length of the track to get the total number of bits
Divide the total number of bits by 8 to get the file size in bytes
If necessary, convert to larger units like kibibytes, mebibytes, etc

A sound clip uses 48KHz sample rate, 24 bit resolution and is 30 seconds long.

48000 x 24 = 1152000 bits per second x 30 = 34560000 bits for the whole clip

34560000 ÷ 8 = 4320000 bytes ÷ 1024 = 4218.75 kibibytes ÷ 1024 = 4.12 mebibytes

Remember to always use the units specified in the question when giving the final answer.

Data Storage (CIE IGCSE Computer Science)