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J277 1.2.4 Hexadecimal conversion
Part 3 of 5 · J277 1.2.4 · Number systems
Hexadecimal, taught through the exact relationship between one hex digit and one group of four bits.
Students will:
- explain why hexadecimal is used alongside binary
- recall the hexadecimal digits A to F
- convert between 8-bit binary and two hexadecimal digits
- convert between denary 0 to 255 and hexadecimal
- complete a table holding all three representations
Inside: 6 text sections, 2 multiple-choice activities, 1 completion activity, 2 written answers, 5 number activities. 25 marks. Suggested teaching time: 40–60 minutes. 1 diagram.
Includes a teacher guide with suggested sections, timings and common misconceptions.
Series: J277 1.2.4 · Number systems, part 3 of 5.
Shared by Coding PathwayVerified teacher
- 16 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 17 Aug 2026
- Updated 27 Oct 2026
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The whole resource, exactly as a class sees it. Answers and marking are held back.
Hexadecimal conversion
Hexadecimal is a shorter way for people to write binary values. One hex digit represents exactly four bits. You will convert between denary 0–255, eight-bit binary and two-digit hexadecimal.
1. Sixteen digit symbols
Hexadecimal is base 16. Its digits are 0–9 and A–F.
| Denary | Hex | Denary | Hex |
|---|---|---|---|
| 0 | 0 | 8 | 8 |
| 1 | 1 | 9 | 9 |
| 2 | 2 | 10 | A |
| 3 | 3 | 11 | B |
| 4 | 4 | 12 | C |
| 5 | 5 | 13 | D |
| 6 | 6 | 14 | E |
| 7 | 7 | 15 | F |
A–F are single digits. F has denary value 15; it is not the greatest two-digit hex value. Two-digit values run from 00 to FF.
- A
- B
- C
- D
- E
- F
Why is hexadecimal useful when a person reads or copies a binary value?
- AIt removes the need for binary inside a computer
- BIt compresses every file
- CIt uses fewer written digits for the same value
- DIt can only represent values below 16
2. One nibble at a time
Split an eight-bit number into two nibbles of four bits. Convert each nibble and keep their order.
10111100 becomes 1011 1100, then B C: hexadecimal BC.
To reverse this, replace each hex digit with four bits: 3D becomes 0011 1101. Keep four positions even if a nibble starts with zeros.
Convert to two-digit hexadecimal.
a)Convert 10100000 to hexadecimal, one nibble at a time.
b)Convert 00001110 to hexadecimal, one nibble at a time.
Convert to eight-bit binary.
a)Convert 4D to binary, one nibble at a time.
b)Convert 06 to binary, one nibble at a time.
A student writes binary 10110000 as hexadecimal B. Which correction is needed?
- AReverse the nibbles to give 0B
- BKeep the zero nibble at the right: B0
- CReplace B with F
- DRead the bits as denary digits
3. Hexadecimal and denary
Two-digit hexadecimal uses place values 16 and 1. For B4, B means 11, so (11 × 16) + 4 = 180.
For denary to hex, find the number of complete sixteens and the remainder. For 126: seven sixteens and remainder 14 gives 7E.
Converting through eight-bit binary is also valid.
Convert each hexadecimal value to denary.
a)What is D2 in denary?
b)What is 4B in denary?
Convert each denary value to two-digit hexadecimal.
a)Convert 32 to hexadecimal.
b)Convert 185 to hexadecimal.
Use hexadecimal D6 as an example to explain a method for converting a two-digit hexadecimal value to denary. Include the final value.
Students type their answer here.
4. Choose a route
Complete the missing forms in the table without the headings. Use nibbles between binary and hex, and place values when denary is involved. Every binary answer needs eight bits; every hex answer needs two digits.
Complete the two missing representations in each row.
a)Denary 125. Fill in the binary and hexadecimal.
b)Binary 00101010. Fill in the denary and hexadecimal.
c)Hexadecimal E1. Fill in the denary and binary.
Explain why writing binary 11010000 as hexadecimal D0 is a convenient notation rather than data compression.
Students type their answer here.
Review
Check one conversion in reverse. In particular, check whether a leading zero, a right-hand zero or the nibble order changed.