← IGCSE Computer Science Paper 1

Number bases: denary, binary and hexadecimal

How many different digits a number system uses: denary is base 10 (digits 0-9), binary is base 2 (digits 0-1) and hexadecimal is base 16 (digits 0-9 and A-F).

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 3

Understanding Number bases: denary, binary and hexadecimal in IGCSE Computer Science Paper 1

What it does: The subscript 16 marks hexadecimal. The letter F is a valid hex digit worth 15, so 2F₁₆ is a correct hex number. Denary is base 10 because it uses ten different digits, 0 to 9. A subscript after a number shows its base. 1101₂ is a binary number. Hexadecimal is base 16, so the subscript is 16. A subscript of 10 means denary. A base 2 number can only contain 0 and 1, so 1021₂ is not valid. It could be written as 1011₂ instead.

Common mistakes: Denary uses the ten digits 0 to 9, so it is base 10, not base 8. The hexadecimal digits go from A = 10 up to F = 15. The largest single hex digit is 15, not 16.

Class: _____________________ · Name: _____________________ · Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

🖨 Print worksheet + answer key Add Number bases: denary, binary and hexadecimal to a class →

This module's key terms are also in a printable crossword (Modules 3–17) and word search (Modules 3–27).

Take this worksheet further — free with Cloodit

Each concept is reinforced from every angle — learned, then applied, then tested.

Learning

Duo

Which statement about denary is correct?

Denary is base 10 and uses the digits 0-9Denary is base 2 and uses the digits 0-9

Matches

1021₂

↓

Binary is base 2 so it only has the digits 0 and 1. The digit 2 is not allowed in a binary number.

Applying

Meanings

Term

number base

Meaning

How many different digits a number system uses: denary is base 10 (digits 0-9), binary is base 2 (digits 0-1) and hexadecimal is base 16 (digits 0-9 and A-F).

Practice

Denary: base 10, digits 0-9

Testing

Gaps

Denary is base 10, digits 0 to

Check Answer

Spots

1Denary is base 8

2Digits: 0 to 9

Cloodit turns curriculum-aligned coding content into journeys students work through one biome at a time.

Students earn collectable badges

Over 100 of them, across seven natural biomes.

Study Buddy

Students build a real study resource

Turns their work into revision material ready for Flash Cards and Exam study.

Diamond Dash — one of Cloodit's live, competitive Sprint games

Students lock in with Sprints

Live, competitive practice for the start of the lesson or a teacher-led lesson finisher.

A Cloodit certificate of achievement, ready to personalise and print

Custom printable certificates

Honour your top performers, or encourage a student who's trying hard — ready to print in seconds.

Add to class →

Quick Questions

1. Which statement about denary is correct?

A. Denary is base 2 and uses the digits 0-9

B. Denary is base 10 and uses the digits 0-9 ✓

Denary is base 10 because it uses ten different digits, 0 to 9.

2. Which statement about binary is correct?

A. Binary is base 2 and uses only 0 and 1 ✓

B. Binary is base 8 and uses 0 to 7

Binary is base 2 because it uses just two digits: 0 and 1.

3. Which statement about hexadecimal is correct?

A. Hexadecimal is base 16 and uses 0-9 and A-F ✓

B. Hexadecimal is base 10 and uses 0-9 and A-F

Hexadecimal has 16 different digits: 0 to 9, then A to F, so it is base 16.

4. Which number is written in binary?

A. 102101

B. 101101 ✓

Binary only uses the digits 0 and 1, so 102101 cannot be binary because it contains a 2.

5. Which number could be written in hexadecimal but NOT in denary?

A. 3F ✓

B. 39

The letter F is a hexadecimal digit but is not a denary digit. 39 uses only 0-9, so it is valid in denary.

Match the Pairs

25₁₀ → The number twenty-five written in denary (base 10), which uses the digits 0-9

1011₂ → A binary (base 2) number, which can only use the digits 0 and 1

Hexadecimal is base 16, so it needs 16 different digits: 0-9 and then A-F → 2F₁₆

Denary is base 10, so it uses ten different digits: 0 to 9 → 906₁₀

1021₂ → Binary is base 2 so it only has the digits 0 and 1. The digit 2 is not allowed in a binary number.

4G₁₆ → Hexadecimal only uses the digits 0-9 and the letters A-F. The letter G is not a hex digit.

Key Term

number base

How many different digits a number system uses: denary is base 10 (digits 0-9), binary is base 2 (digits 0-1) and hexadecimal is base 16 (digits 0-9 and A-F).

Fill in the Blanks

1. Denary is base 10, digits 0 to 9

Hint: Type the highest digit that denary uses.

2. Binary is base 2: digits 0 and 1

Hint: Type how many different digits binary uses.

3. Hexadecimal is base 16: digits 0-9, A-F

Hint: Type the last letter used as a hexadecimal digit.

4. The number 1011(2) is written in binary

Hint: Type the base written in brackets after a binary number.

5. 3F(16) is written in hexadecimal

Hint: Type the name of the number system with base 16.

Spot the Error

Question 1

A Denary is base 8

B Digits: 0 to 9

C Binary is base 2

D Digits: 0 and 1

Line A — Denary uses the ten digits 0 to 9, so it is base 10, not base 8.

Question 2

A Hexadecimal is base 16

B Digits 0 to 9 are used

C Then letters A to F

D A stands for 10, F for 16

Line D — The hexadecimal digits go from A = 10 up to F = 15. The largest single hex digit is 15, not 16.

Question 3

A Binary is base 10

B It uses 2 different digits

C The digits are 0 and 1

Line A — Binary uses only 2 different digits, so it is base 2. Base 10 is denary.

Question 4

A Denary is base 10

B It uses 9 different digits

C The digits are 0 to 9

Line B — The digits 0 to 9 are ten different digits, which is why denary is base 10. It should say 10 different digits.

Question 5

A Hexadecimal is base 16

B It uses 16 different digits

C The digits are 0-9 and A-G

Line C — Hexadecimal uses 0-9 and the letters A to F, which makes 16 digits. There is no letter G in hexadecimal.

Student with a class code? Join your class →