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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 explanation cells, 5 number grids, 2 multiple-choice questions, 1 fill-in-the-blanks cell and 2 written answers. 35 marks, about 75 minutes.
Series: J277 1.2.4 · Number systems, part 3 of 5.
Shared by Coding PathwayVerified teacher
- 16 cells
- About 75 minutes
- CC BY-SA 4.0
- Shared 17 Aug 2026
- Updated 9 Sept 2026
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Number systems 3: hexadecimal conversion
Hexadecimal is a compact way to write the same values represented by binary. The key relationship is exact: one hexadecimal digit matches one group of four binary bits.
By the end of this worksheet, you should be able to:
- explain why hexadecimal is used as an alternative representation of binary
- recall the hexadecimal digits A to F
- convert 8-bit binary to 2-digit hexadecimal and back
- convert denary values from 0 to 255 to hexadecimal and back
- complete a conversion table containing all three representations
- explain a conversion method clearly
Work through the explanation, checks and applications in order. Use the final challenge to explain the method as well as use it.
1. Base 16
Hexadecimal is a base 16 number system. It needs sixteen single-digit symbols:
| Denary value | Hex digit | Denary value | Hex digit |
|---|---|---|---|
| 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 to F are single hexadecimal digits. For example, F means denary 15. It does not mean the letter F is being stored.
The OCR range for this topic is 00 to FF, matching binary 00000000 to 11111111 and denary 0 to 255.
- F
- B
- 12
- A
- E
- D
- C
- 16
Why is hexadecimal often used when people need to read or write binary values?
- AHexadecimal allows a computer to stop using binary internally
- BHexadecimal always compresses the stored file
- CHexadecimal can represent only smaller values than binary
- DHexadecimal uses fewer digits for the same value, making it easier to read and less likely to be copied incorrectly
2. Binary and hexadecimal, nibble by nibble
One hexadecimal digit maps to exactly four binary bits, called a nibble. An 8-bit number therefore maps to two hexadecimal digits.
Example: convert 10111100 to hexadecimal.
- Split it into nibbles:
1011 1100 - Convert each nibble separately:
1011 = Band1100 = C - Keep the order:
BC
To reverse the process, replace each hex digit with four bits.
Example: 3D becomes 0011 1101.
Always write four bits for each hex digit. F is 1111, not 1101.
Convert each 8-bit binary number to 2-digit hexadecimal.
Split the binary number into two 4-bit nibbles and convert each nibble without changing their order.
a)Convert 10111000 to hexadecimal, one nibble at a time.
b)Convert 01001101 to hexadecimal, one nibble at a time.
c)Convert 10011010 to hexadecimal, one nibble at a time.
Convert each 2-digit hexadecimal value to 8-bit binary.
Replace each hexadecimal digit with exactly four bits, including any leading zeros within a nibble.
a)Convert A6 to binary, one nibble at a time.
b)Convert C0 to binary, one nibble at a time.
c)Convert FB to binary, one nibble at a time.
A student converts 10110000 to hexadecimal B. What is the error?
- AB must be replaced with F because every 1 bit is hexadecimal F
- BThe right-hand nibble 0000 must be written as the second hex digit 0, so the answer is B0
- CThe binary number should be read as the denary number 10,110,000
- DThe answer should be 0B because the nibbles must be reversed
3. Hexadecimal and denary
A 2-digit hexadecimal number has place values 16 and 1.
Example: convert B4 to denary.
- B has value 11
(11 × 16) + 4 = 180
To convert denary to 2-digit hexadecimal:
- Divide the value into groups of 16.
- Write the number of complete sixteens as the left digit.
- Write the remainder as the right digit.
- Replace values 10 to 15 with A to F.
Example: 126 contains 7 complete sixteens with remainder 14, so it is 7E.
You may also convert through 8-bit binary. Both methods are valid when they are carried out accurately.
Convert each 2-digit hexadecimal value to denary.
Multiply the value of the left digit by 16, then add the value of the right digit.
a)What is 1E in denary?
b)What is A2 in denary?
c)What is C7 in denary?
Convert each denary value to 2-digit hexadecimal.
Find the number of complete sixteens and the remainder. Convert 10 to 15 into A to F.
a)Convert 71 to hexadecimal.
b)Convert 154 to hexadecimal.
c)Convert 169 to hexadecimal.
Use the hexadecimal value C7 as an example to explain how to convert a 2-digit hexadecimal number directly to denary. Show the calculation and final answer.
State the denary value of C, apply the 16 and 1 place values, then add.
Students type their answer here.
4. Bring the three representations together
The next table may give you a denary, binary or hexadecimal value. Complete the two missing representations.
Choose the shortest reliable route:
- binary and hexadecimal: convert nibble by nibble
- binary and denary: use the binary place values
- hexadecimal and denary: use the 16 and 1 place values, or move through binary
Check that every binary answer has 8 bits and every hexadecimal answer has 2 digits.
Complete the missing denary, 8-bit binary and 2-digit hexadecimal representations.
Keep nibble order unchanged and include every leading zero required by the stated width.
a)Hexadecimal CE. Fill in the denary and binary.
b)Denary 104. Fill in the binary and hexadecimal.
c)Hexadecimal 59. Fill in the denary and binary.
d)Hexadecimal 31. Fill in the denary and binary.
Challenge: a student claims that changing 11110000 into F0 compresses the data from eight bits to two bits. Evaluate the claim.
Distinguish the number of written symbols from the value and its binary representation inside the computer.
Students type their answer here.
Closed-book review
From memory, write:
- A through F with their denary values.
- The four-bit binary form of A, B, C, D, E and F.
- One reason hexadecimal is used.
- The method for binary to hexadecimal.
- The method for hexadecimal to denary.
Then reverse one answer as a check. If a right-hand zero disappears or a nibble has fewer than four bits, correct the width before moving on.