Community resourceWorksheet
J277 1.2.4 Binary and denary conversion
Part 2 of 5 · J277 1.2.4 · Number systems
Conversion in both directions, starting with visible place values and removing the prompts as the worksheet goes on.
Students will:
- convert an 8-bit binary number into denary
- convert a denary whole number into 8-bit binary
- include leading zeros when an 8-bit answer is required
- check a conversion by reversing it
- explain the method clearly
Inside: 5 explanation cells, 4 number grids, 4 multiple-choice questions and 3 written answers. 25 marks, about 75 minutes.
Series: J277 1.2.4 · Number systems, part 2 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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The whole resource, exactly as a class sees it. Answers and marking are held back.
Number systems 2: converting binary and denary
Conversion is not a guessing task. Every binary position has a known value, so you can build an answer and check it. This worksheet begins with visible place values and gradually removes the prompts.
By the end of this worksheet, you should be able to:
- convert an 8-bit binary number into denary
- convert a positive denary whole number into 8-bit binary
- include leading zeros when an 8-bit answer is required
- check a conversion by reversing the process
- 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.
Which list gives the 8-bit binary place values from left to right?
- A128, 64, 32, 16, 8, 4, 2, 1
- B1, 2, 4, 8, 16, 32, 64, 128
- C80, 70, 60, 50, 40, 30, 20, 10
- D256, 128, 64, 32, 16, 8, 4, 2
1. Binary to denary
Use this method:
- Write or read the place values above the bits.
- Select each place value whose bit is 1.
- Add those place values.
Example: convert 10100110 to denary.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
128 + 32 + 4 + 2 = 166
A 0 does not add its place value.
Convert each 8-bit binary number to denary.
Add the place values above the columns that contain a 1.
a)What is 00011011 in denary?
b)What is 00011111 in denary?
c)What is 10111000 in denary?
A student says 01010001 is 49 because they calculate 32 + 16 + 1. What should they correct?
- ARemove the final 1 because the LSB has no value
- BRead the digits as the denary number 10,100,001
- CUse 64 for the second column, giving 64 + 16 + 1 = 81
- DAdd every place value, including columns containing 0
2. Denary to 8-bit binary
Build the denary value from the largest useful place value downward.
Example: convert 90 to 8-bit binary.
- 90 contains 64, leaving 26. Put 1 in the 64 column.
- 26 contains 16, leaving 10. Put 1 in the 16 column.
- 10 contains 8, leaving 2. Put 1 in the 8 column.
- 2 contains 2, leaving 0. Put 1 in the 2 column.
- Put 0 in every unused column.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
So 90 is 01011010. Add the 1 columns to check: 64 + 16 + 8 + 2 = 90.
Convert each denary number to 8-bit binary.
Choose place values that total the denary value, then put 0 in every unused column.
a)Convert 236 to 8-bit binary.
b)Convert 93 to 8-bit binary.
c)Convert 151 to 8-bit binary.
A question asks for 26 as an 8-bit binary number. Which answer meets the instruction?
- A00011010
- B11010
- C0011010
- D00011011
3. Remove the scaffolding
You now know both methods. For the next two tasks, the place-value headings are hidden. Write 128, 64, 32, 16, 8, 4, 2, 1 on the scratch row if you need them.
Use a reverse check after each answer:
- after binary to denary, rebuild the value in 8-bit binary
- after denary to binary, add the place values containing a 1
Checking is part of a reliable method, not a sign that you are unsure.
Independent check: convert each binary number to denary.
Recreate the place values on the scratch row if needed, then check by reversing the conversion.
a)What is 11000001 in denary?
b)What is 11001010 in denary?
c)What is 01111110 in denary?
Independent check: convert each denary number to 8-bit binary.
All eight bit positions must be completed, including leading zeros.
a)Convert 38 to 8-bit binary.
b)Convert 176 to 8-bit binary.
c)Convert 37 to 8-bit binary.
A student converts 150 to 10010110. Explain how to check whether the conversion is correct, then give the result of the check.
Add the place values containing a 1 and compare the total with the original denary number.
Students type their answer here.
Describe a method for converting a positive denary whole number into 8-bit binary.
Give the stages in order. Include place values, remaining value, unused columns and the 8-bit width.
Students type their answer here.
Challenge: the digit sequence 101 has value 101 in denary but value 5 in binary. Explain why the same written digits represent different values in the two number systems.
Compare the place values in base 10 with those in base 2.
Students type their answer here.
Which is the strongest way to check a denary-to-binary conversion?
- ACount the 1 bits and use the count as the denary answer
- BRemove every leading zero and assume the remaining digits are correct
- CRead the binary digits as if they were a denary number
- DAdd the place values containing a 1 and compare the total with the original denary number
Closed-book review
Write the eight place values from memory. Then answer these prompts:
- Binary to denary: I...
- Denary to binary: I...
- An 8-bit answer needs...
- I can check a conversion by...
If your independent answers were less accurate than the supported ones, repeat one question with the headings visible and one without them. The goal is dependable reasoning, not speed.