1.1

Number systems

Cambridge IGCSE Computer Science (0478)  · Unit 1: Data representation  · 10 flashcards

Number systems is topic 1.1 in the Cambridge IGCSE Computer Science (0478) syllabus , positioned in Unit 1 — Data representation , alongside Text, sound and images and Data storage and compression.  In one line: Binary is a number system that uses only two digits: 0 and 1. It's base 2, meaning each digit position represents a power of 2 (.

This topic is examined in Paper 1 (computer systems theory) and Paper 2 (algorithms, programming and logic).

The deck below contains 10 flashcards — 6 definitions, 1 key concept and 1 application card — covering the precise wording mark schemes reward.  Use the 6 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

The term 'binary' and state its base

Binary is a number system that uses only two digits: 0 and 1. It's base 2, meaning each digit position represents a power of 2 (

Example: 2^0, 2^1, 2^2).

What the Cambridge 0478 syllabus says

Official 2026-2028 spec

These are the exact learning objectives Cambridge sets for this topic. Match the command word (Describe, Explain, State, etc.) in your answer to score full marks.

  1. Understand Understand how and why computers use binary to represent all forms of data
  2. Understand Understand the denary, binary and hexadecimal number systems
  3. Convert Convert between positive denary and positive binary, positive denary and positive hexadecimal, positive hexadecimal and positive binary
  4. Understand Understand how and why hexadecimal is used as a beneficial method of data representation
  5. Add Add two positive 8-bit binary integers
  6. Understand Understand the concept of overflow and why it occurs in binary addition
  7. Perform Perform a logical binary shift on a positive 8-bit binary integer and understand the effect this has on the positive binary integer
  8. Use Use two's complement to represent positive and negative 8-bit binary integers
Definition Flip

Define the term 'binary' and state its base.

Answer Flip

Binary is a number system that uses only two digits: 0 and 1. It's base 2, meaning each digit position represents a power of 2 (

Example: 2^0, 2^1, 2^2).
Definition Flip

Explain what 'denary' number system is and give another common name for it.

Answer Flip

Denary is the base-10 number system that humans commonly use. Each digit position represents a power of 10 (

Example: 10^0, 10^1, 10^2). It is also commonly called 'decimal'.
Definition Flip

Describe the hexadecimal number system and its base.

Answer Flip

Hexadecimal is a base-16 number system. It uses the digits 0-9 and the letters A-F to represent values from 0 to 15 (A=10, B=11, C=12, D=13, E=14, F=15).

Key Concept Flip

Convert the binary number 1011 to denary.

Answer Flip

1011 in binary is (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11 in denary.

Key Concept Flip

Convert the denary number 25 to hexadecimal.

Answer Flip

25 divided by 16 is 1 with a remainder of 9. Therefore, 25 in denary is 19 in hexadecimal.

Definition Flip

Define the term 'bit'.

Answer Flip

A bit is the smallest unit of data in a computer, representing a single binary digit (0 or 1). It is the fundamental building block of all digital information.

Definition Flip

Define the term 'byte' and how many bits are in one byte.

Answer Flip

A byte is a unit of digital information that consists of 8 bits. Bytes are commonly used to represent characters, numbers, and other data in computer systems.

Definition Flip

Define the term 'nibble' and state how many bits is in one nibble.

Answer Flip

A nibble is a unit of digital information that consists of 4 bits. It is exactly half of a byte and is used in some applications.

Key Concept Flip

Give an example of where hexadecimal numbers are used in computing.

Answer Flip

Hexadecimal numbers are commonly used to represent memory addresses and colours in HTML and CSS.

Example: a color code might be '#FFFFFF' (white).
Key Concept Flip

Explain why computers use the binary number system.

Answer Flip

Computers use binary because electronic circuits have two distinct states, often represented by 'on' or 'off', which can easily represent 1 and 0. This simplifies the design and operation of computer hardware.

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1.2 Text, sound and images

Key Questions: Number systems

Define the term 'binary' and state its base.

Binary is a number system that uses only two digits: 0 and 1. It's base 2, meaning each digit position represents a power of 2 (

Example: 2^0, 2^1, 2^2).
Explain what 'denary' number system is and give another common name for it.

Denary is the base-10 number system that humans commonly use. Each digit position represents a power of 10 (

Example: 10^0, 10^1, 10^2). It is also commonly called 'decimal'.
Describe the hexadecimal number system and its base.

Hexadecimal is a base-16 number system. It uses the digits 0-9 and the letters A-F to represent values from 0 to 15 (A=10, B=11, C=12, D=13, E=14, F=15).

Define the term 'bit'.

A bit is the smallest unit of data in a computer, representing a single binary digit (0 or 1). It is the fundamental building block of all digital information.

Define the term 'byte' and how many bits are in one byte.

A byte is a unit of digital information that consists of 8 bits. Bytes are commonly used to represent characters, numbers, and other data in computer systems.

More topics in Unit 1 — Data representation

Number systems sits alongside these Computer Science decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

1.2 Text, sound and images

10 flashcards
1.3 Data storage and compression

9 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0478 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

binary denary hexadecimal convert base 2 base 10 base 16 bit byte nibble

Key terms covered in this Number systems deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

The term 'binary' and state its base
Explain what 'denary' number system is and give another common name for it
Describe the hexadecimal number system and its base
The term 'bit'
The term 'byte' and how many bits are in one byte
The term 'nibble' and state how many bits is in one nibble

How to study this Number systems deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.