Data Storage | Computer for GCSE/IGCSE - Year 11 PDF Download

Data Storage

• Data storage is measured in various units, each indicating different storage capacities.
• The smallest unit is the bit, representing a single binary digit (0 or 1).
• A nibble consists of 4 bits, while a byte comprises 8 bits.
• Larger units include Kibibyte (KiB), Mebibyte (MiB), Gibibyte (GiB), Tebibyte (TiB), Pebibyte (PiB), and Exbibyte (EiB).
• For example, 1 KiB equals 2¹⁰ bytes, 1 MiB equals 2²⁰ bytes, 1 GiB equals 2³⁰ bytes, 1 TiB equals 2⁴⁰ bytes, 1 PiB equals 2⁵⁰ bytes, and 1 EiB equals 2⁶⁰ bytes.

Calculating Image File Size

• Determine the resolution of the image in pixels (width x height): This involves finding out how many pixels the image has in total.
• Determine the colour depth in bits (e.g. 8 bits for 256 colours): Understand the number of bits used to represent colors in the image.
• Multiply the number of pixels by the colour depth to get the total number of bits: Calculate the total bits required to store the image.
• Divide the total number of bits by 8 to get the file size in bytes: Convert the total bits to bytes for the file size.
• If necessary, convert to larger units like kibibytes, mebibytes, etc: Adjust the file size to larger units if needed for better understanding.

Calculating Image File Size Walkthrough

• An example scenario could be an image that measures 100 by 80 pixels and uses 128 colors, which corresponds to 7 bits. 
• By multiplying 100 x 80 x 7, we get 56000 bits. 
• Dividing 56000 by 8 gives us 7000 bytes, which is approximately 6.84 kibibytes.

Understanding File Size Calculation for Sound Files

To determine the file size of a sound file, follow these steps:

• Determine the sample rate in Hertz (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 obtain 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 derive the file size in bytes
• If needed, convert the file size to larger units like kibibytes, mebibytes, etc.

Calculating sound file size walkthrough

• Sample Rate and Resolution:  A sound clip with a 48KHz sample rate and 24-bit resolution is considered.
• Duration of the Clip: The sound clip is 30 seconds long.
• Calculations: Firstly, we calculate the total number of bits for the entire clip.
  • 48000 x 24 = 1152000 bits per second
  • 1152000 bits per second x 30 seconds = 34560000 bits
  • Next, converting bits to bytes and further to kilobytes and megabytes:
  • 34560000 bits ÷ 8 = 4320000 bytes
  • 4320000 bytes ÷ 1024 = 4218.75 kibibytes
  • 4218.75 kibibytes ÷ 1024 = 4.12 mebibytes