Data Storage and Compression

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand how data storage is measured (including: bit, nibble, byte, kibibyte, mebibyte, gibibyte, tebibyte, pebibyte, exbibyte, and the relationships between them)
  2. Calculate the file size of image files and sound files using information given
  3. Understand the purpose of and need for data compression
  4. Understand how files are compressed using lossy and lossless compression methods

1. How Data Storage is Measured

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Basic Units of Data Storage

Computers store all information as binary digits – that means 0s and 1s. We need units to measure how much data we can store, just like we use meters to measure distance or kilograms to measure weight.

Here are the basic building blocks:

Bit (b)

  • A bit is short for "binary digit"
  • It is the smallest unit of data in a computer
  • A bit can only be one of two values: 0 or 1
  • Think of it like a light switch – it's either off (0) or on (1)

Nibble

  • A nibble is a group of 4 bits
  • Example: 1010 is a nibble
  • Nibbles aren't used as much as other units, but it's useful to know they exist

Byte (B)

  • A byte is a group of 8 bits
  • This is the smallest unit of memory that a computer uses to store information
  • Example: 10110101 is one byte
  • One byte can represent a single character, like the letter 'A'
  • Important relationship: 8 bits = 1 byte

Larger Units of Data Storage

As files and programs get bigger, we need larger units to measure them. Just like we use kilometers instead of meters for long distances, we use larger units for big amounts of data.

The system uses powers of 2 and multiples of 1024 (not 1000, which is important for calculations).

UnitSymbolValueExplanation
KibibyteKiB1,024 bytes2^10 bytes
MebibyteMiB1,024 KiB2^20 bytes (1,048,576 bytes)
GibibyteGiB1,024 MiB2^30 bytes (1,073,741,824 bytes)
TebibyteTiB1,024 GiB2^40 bytes
PebibytePiB1,024 TiB2^50 bytes
ExbibyteEiB1,024 PiB2^60 bytes

Important Relationships to Remember

  • 8 bits = 1 byte
  • 1024 bytes = 1 kibibyte (KiB)
  • 1024 kibibytes = 1 mebibyte (MiB)
  • 1024 mebibytes = 1 gibibyte (GiB)
  • 1024 gibibytes = 1 tebibyte (TiB)
  • 1024 tebibytes = 1 pebibyte (PiB)
  • 1024 pebibytes = 1 exbibyte (EiB)

Converting Between Units

When you need to convert between units, follow these simple rules:

Converting to a SMALLER unit (going down) → MULTIPLY

  • Bytes to bits: multiply by 8
  • MiB to KiB: multiply by 1024
  • GiB to MiB: multiply by 1024

Example: Convert 3 MiB to KiB

  • 3 × 1024 = 3,072 KiB

Converting to a LARGER unit (going up) → DIVIDE

  • Bits to bytes: divide by 8
  • KiB to MiB: divide by 1024
  • MiB to GiB: divide by 1024

Example: Convert 2000 KiB to MiB

  • 2000 ÷ 1024 = 1.95 MiB

Real-World Context

To help you understand the scale:

  • A typical photo from your phone might be 3-4 MiB
  • A modern hard drive might be 1-2 TiB, which could store over half a million photos
  • Streaming a video might use 4 MiB per second of data

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