Binary Prefixes (Cambridge (CIE) A Level Computer Science): Revision Note

Binary prefixes

What is a binary prefix?

• A binary prefix is a unit prefix used to indicate multiples of bytes in binary

• Consider the word kilobyte, "kilo" is the prefix

• The byte is the standard unit used for measuring data storage, so there needs to be a way of expressing bytes in larger multiples

Denary prefixes

• A common way of expressing multiples of bytes is to use denary prefixes:

• This system relies on the assumption that 1 kilo = 1000

• This assumption is based on the denary (base 10) number system

  • E.g. a 1 GB hard drive can store 1 x 10⁹ bytes

Binary prefixes

• However, computers use the binary (base 2) number system so the denary system is technically inaccurate when describing storage

• To be precise, expressing multiples of bytes is done using binary prefixes:

• Notice the prefixes change depending on the system being used, e.g. kilo (denary) vs kibi (binary)

Why does it matter?

• The importance of the system being used depends on how precise you need to be

• When precision is required (e.g. identifying RAM), binary prefixes should be used

  • E.g. 16 GiB RAM can store 16 × 2³⁰ bytes (17,179,869,184 bytes)

• When a rough estimate is acceptable (e.g. describing storage device capacity), denary prefixes are commonly used

  • E.g. a 16 GB memory stick can store 16 × 10⁹ bytes (16,000,000,000 bytes)