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 text sections, 3 multiple-choice activities, 2 written answers, 4 number activities. 16 marks. Suggested teaching time: 40–55 minutes.
Includes a teacher guide with suggested sections, timings and common misconceptions.
Series: J277 1.2.4 · Number systems, part 2 of 5.
Shared by Coding PathwayVerified teacher
- 14 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 17 Aug 2026
- Updated 27 Oct 2026
Preview
The whole resource, exactly as a class sees it. Answers and marking are held back.
Binary and denary conversion
Use place values to convert a value, then reverse the conversion to check it. The first practice shows the headings; later practice asks you to recall them.
Which list gives eight-bit 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
Select the place values containing 1 and add them.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
For 10100110, the total is 128 + 32 + 4 + 2 = 166. Columns containing 0 add nothing.
Convert each number to denary.
Use the visible headings to select the 1 columns.
a)What is 10010010 in denary?
b)What is 00100101 in denary?
A student converts 01010001 using 32 + 16 + 1. Which correction is needed?
- ARemove the final 1
- BRead the digits as a denary number
- CUse 64 for the second column, giving 64 + 16 + 1
- DAdd all columns, including the zeros
2. Denary to binary
Work from the largest place value down. Put 1 where you use a value, subtract it, and put 0 in each unused position.
For 90: use 64 (26 left), 16 (10 left), 8 (2 left), then 2 (0 left).
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
The result is 01011010. Check: 64 + 16 + 8 + 2 = 90.
Convert each denary value to eight-bit binary.
Use the headings and complete every position.
a)Convert 74 to 8-bit binary.
b)Convert 129 to 8-bit binary.
Which answer gives 26 using exactly eight bits?
- A11010
- B0011010
- C00011010
- D00011011
3. Work independently
The headings are now hidden. You can recreate them on the scratch row. Check each conversion by reversing it.
Convert these eight-bit numbers to denary.
a)What is 11000101 in denary?
b)What is 00000001 in denary?
Convert these values to eight-bit binary.
a)Convert 23 to 8-bit binary.
b)Convert 255 to 8-bit binary.
A student converts 150 to 10010110. Explain how to check this answer and what the check shows.
Students type their answer here.
Describe a method for converting a denary whole number from 0 to 255 into eight-bit binary.
Students type their answer here.
Review
Improve one independent conversion using a reverse check. If you needed the headings, try the same method once more without them.