Community resourceWorksheet
1CP2-P-2.5 Hexadecimal and binary
Part 5 of 7 · 1CP2-P-2 · Signed data and encoding
The hexadecimal worksheet, built on the nibble mapping so conversion never becomes guesswork.
Students will:
- recall the mapping between a four-bit nibble and one hexadecimal digit
- convert 8-bit binary to two hexadecimal digits
- convert two hexadecimal digits to 8-bit binary
- explain why programmers write long binary values in hexadecimal
- correct a conversion presented at the wrong width
Inside: 7 explanation cells, 2 multiple-choice questions, 3 number cells, 1 fill-in-the-blanks cell and 2 written answers. 19 marks, about 45 minutes.
Series: 1CP2-P-2 · Signed data and encoding, part 5 of 7.
Shared by Coding PathwayVerified teacher
- 15 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 17 Aug 2026
Preview
The whole resource, exactly as a class sees it. Answers and marking are held back.
Hexadecimal and binary
Hexadecimal is base 16. Its digits are 0–9 followed by A–F, representing values 10–15. One hexadecimal digit maps exactly to four binary bits, called a nibble.
1. Learn the nibble mapping
| Hex | Binary | Hex | Binary |
|---|---|---|---|
| 0 | 0000 | 8 | 1000 |
| 1 | 0001 | 9 | 1001 |
| 2 | 0010 | A | 1010 |
| 3 | 0011 | B | 1011 |
| 4 | 0100 | C | 1100 |
| 5 | 0101 | D | 1101 |
| 6 | 0110 | E | 1110 |
| 7 | 0111 | F | 1111 |
Convert each nibble independently. Do not treat the complete binary pattern as one denary conversion unless checking.
- 10
- 15
- 1010
- 1111
2. Binary to hexadecimal
Group from the right into four-bit nibbles: 0110 1101. Convert independently: 0110 = 6, 1101 = D. Therefore 01101101 = 6D in hexadecimal.
Keep leading zeroes inside each nibble while converting.
Convert each 8-bit binary pattern to two hexadecimal digits.
Work one four-bit nibble at a time.
a)Convert 00111110 to hexadecimal, one nibble at a time.
b)Convert 10100111 to hexadecimal, one nibble at a time.
c)Convert 11010010 to hexadecimal, one nibble at a time.
3. Hexadecimal to binary
Expand every hexadecimal digit to exactly four bits. B4 becomes 1011 0100. Writing only 1011 100 loses the fixed nibble boundary and is not an 8-bit answer.
Convert each two-digit hexadecimal value to 8-bit binary.
Write four bits for every hexadecimal digit, including leading zeroes.
a)Convert 5C to binary, one nibble at a time.
b)Convert E1 to binary, one nibble at a time.
c)Convert 9A to binary, one nibble at a time.
4. Why hexadecimal is used
Hexadecimal is a shorthand for binary: four bits become one digit. The shorter form is easier for people to read, copy, remember and check, reducing transcription mistakes.
It does not make the underlying data take less storage. The computer still stores binary; only the human-facing notation changes.
Explain why a programmer might write a long binary value in hexadecimal. Your answer must include the relationship between the two representations and one human benefit.
Avoid claiming that hexadecimal saves computer storage.
Students type their answer here.
Which statement about hexadecimal is correct?
- AIt compresses every file to half its size.
- BIt changes the bits stored by the computer.
- CIt is a compact notation for the same binary pattern.
- DIt can represent only positive denary values below 16.
5. Independent mixed conversion
Do not convert through denary unless using it as a check. Preserve nibble boundaries and write the requested width.
Convert these binary patterns to hexadecimal without displayed nibble place values.
Split into nibbles mentally or in separate working.
a)Convert 01111011 to hexadecimal, one nibble at a time.
b)Convert 11001110 to hexadecimal, one nibble at a time.
A student converts hexadecimal 4D to binary as 1001101. Identify the presentation error and give the correct 8-bit pattern.
Each hexadecimal digit must expand to four bits.
Students type their answer here.
How many hexadecimal digits are needed to represent an 8-bit pattern?
- A1
- B2
- C4
- D8
Route forward
You can now convert directly between binary and hexadecimal and explain why the shorthand is useful. Next, bit patterns encode characters using a character set.