IGCSE · Practice questions · Hexadecimal and where it is used

Four bits per digit.

Six original Cambridge-style questions on hexadecimal conversions and uses, with worked solutions.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Group in fours.

Digits: 0 to 9, then A = 10 up to F = 15.
Binary to hex: split into groups of 4 from the right; convert each group.
Hex to denary: multiply each digit by 16 or 1 (or 256, 4096 for longer numbers) and add.
Why hex: shorter, easier for humans to read and write, fewer errors; the computer still uses binary.

Convert

[2 marks]

Convert the binary number 1010 1111 0011 to hexadecimal.

1010 = A, 1111 = F, 0011 = 3. ✓
AF3. ✓

Convert

[2 marks]

Convert the hexadecimal number 7B to denary. Show your working.

7 × 16 = 112; B = 11. ✓
112 + 11 = 123. ✓

Convert

[2 marks]

Convert the denary number 172 to hexadecimal.

172 = 1010 1100 in binary (128 + 32 + 8 + 4). ✓
1010 = A, 1100 = C, so AC. ✓

Explain

[2 marks]

Give two reasons why hexadecimal is used by programmers instead of binary.

It is shorter, so it is quicker to read and write. ✓
It is easier to understand and fewer errors are made when copying it, and it converts easily to binary (4 bits per digit). ✓

Apply

[3 marks]

A web page uses the colour code #33CC99. Give the denary value of the red, green and blue components.

Red 33 = 3 × 16 + 3 = 51. ✓
Green CC = 12 × 16 + 12 = 204. ✓
Blue 99 = 9 × 16 + 9 = 153. ✓

Recall

[3 marks]

Identify three uses of hexadecimal in computer science.

HTML / web colour codes. ✓
MAC addresses. ✓
Error codes, memory dumps or IPv6 addresses (any one). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.