1.1 Data Representation

2026 Syllabus Objectives

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

  • understand binary magnitudes and the difference between binary prefixes and decimal prefixes
  • understand and use kibi and kilo, mebi and mega, gibi and giga, tebi and tera
  • understand different number systems: binary, denary, hexadecimal, BCD, one’s complement, and two’s complement
  • convert an integer value from one number base or representation to another
  • perform binary addition and binary subtraction
  • understand how overflow happens
  • describe practical uses of BCD and hexadecimal
  • understand how characters are stored in binary using ASCII, extended ASCII, and Unicode

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1. Binary magnitudes and memory units

Computers store data using binary, which means everything is stored using only 0 and 1. Because computers work in binary, memory sizes are closely linked to powers of 2.

A bit is a single binary digit. It can only be 0 or 1.

A byte is usually 8 bits. Bytes are used to measure how much data is stored.

When memory becomes large, we need bigger units. This is where students often get confused, because there are two systems for naming memory sizes:

  • decimal prefixes, based on powers of 10
  • binary prefixes, based on powers of 2

These names look similar, but they do not mean the same thing.

Decimal prefixes

Decimal prefixes are based on the denary number system, which is base 10.

  • 1 kilobyte (KB) = 1000 bytes
  • 1 megabyte (MB) = 1,000,000 bytes
  • 1 gigabyte (GB) = 1,000,000,000 bytes
  • 1 terabyte (TB) = 1,000,000,000,000 bytes

These are often used when talking about storage devices in a general way, such as a hard drive or memory stick.

Binary prefixes

Binary prefixes are based on powers of 2, which matches the way computers actually work internally.

  • 1 kibibyte (KiB) = 1024 bytes = (2^{10})
  • 1 mebibyte (MiB) = 1,048,576 bytes = (2^{20})
  • 1 gibibyte (GiB) = 1,073,741,824 bytes = (2^{30})
  • 1 tebibyte (TiB) = 1,099,511,627,776 bytes = (2^{40})

Why this matters

The difference matters because 1000 and 1024 are not the same.

For example:

  • 1 KB means 1000 bytes
  • 1 KiB means 1024 bytes

So kilo and kibi are different. The same idea applies to:

  • mega vs mebi
  • giga vs gibi
  • tera vs tebi

A good exam point is this:

  • decimal prefixes are based on powers of 10
  • binary prefixes are based on powers of 2

Another good point is:

  • RAM should be described accurately using binary prefixes, such as GiB
  • storage devices are often sold using decimal prefixes, such as GB

2. Number systems

A number system is a way of writing numbers using a set of digits and place values.

The syllabus requires you to know these number systems and representations:

  • denary
  • binary
  • hexadecimal
  • BCD
  • one’s complement
  • two’s complement

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