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J277 1 Paper 1 calculations and working
Part 2 of 5 · J277 Paper 1 · Exam transition
Non-calculator Paper 1 arithmetic, practised with the working set out the way a marker needs to see it.
Students will:
- convert between denary, binary and hexadecimal
- add binary numbers and handle a carry
- carry out left and right binary shifts
- calculate image and sound file sizes with the correct units
- check whether an answer is a sensible size
Inside: 7 explanation cells, 3 number grids, 2 multiple-choice questions and 4 written answers. 36 marks, about 60 minutes.
Series: J277 Paper 1 · Exam transition, part 2 of 5.
Shared by Coding PathwayVerified teacher
- 16 cells
- About 60 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.
Paper 1 exam transition 2: calculations and working
OCR Paper 1 is non-calculator. The arithmetic is designed to be manageable, but marks can depend on selecting the correct values, using the correct units and showing a method.
This worksheet practises:
- denary, binary and hexadecimal conversion
- binary addition and carries
- binary shifts
- image and sound file-size calculations
- data-unit conversions
- checking whether an answer is sensible
The contexts use a fictional digital exhibition. Write every step that helps another person follow your method.
1. Represent the same value
An 8-bit binary pattern has place values 128, 64, 32, 16, 8, 4, 2, 1. Hexadecimal uses sixteen symbols: 0 to 9 and A to F. One hexadecimal digit represents four binary bits, so an 8-bit value maps to two hexadecimal digits.
Leading zeros do not change the value, but include them when the required format is 8-bit binary or 2-digit hexadecimal.
Complete each row so the denary, 8-bit binary and 2-digit hexadecimal forms represent the same value.
Use place values or split the binary into two nibbles. Include leading zeros.
a)Hexadecimal 7E. Fill in the denary and binary.
b)Hexadecimal F8. Fill in the denary and binary.
c)Denary 243. Fill in the binary and hexadecimal.
d)Hexadecimal 0E. Fill in the denary and binary.
2. Binary addition
Work from right to left and show carries.
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 1 = 10, so write 0 and carry 1
- 1 + 1 + 1 = 11, so write 1 and carry 1
Converting to denary can check the final value, but it does not replace the binary working when the question asks you to complete binary addition.
Add each pair of 8-bit binary numbers and show every carry.
Start at the right. Enter each result bit and place a carry in the column it enters.
a)Add these 8-bit binary numbers: 01100000 + 01110011.
b)Add these 8-bit binary numbers: 00010110 + 00111101.
c)Add these 8-bit binary numbers: 00011001 + 00001001.
3. Binary shifts
A left shift moves every bit left and inserts zeros on the right. If no important bit is lost, shifting left by one place multiplies the value by 2; shifting left by three places multiplies it by 8.
A right shift moves every bit right and inserts zeros on the left. For whole-number values, a right shift may discard bits. Describe the actual result shown rather than claiming that every division is exact.
Identify the direction and number of places used in each 8-bit shift.
Track the positions of the 1 bits. Give both the direction and number of places.
a)00111110 became 00000111. Which shift was applied, and by how many places?
b)11001001 became 00011001. Which shift was applied, and by how many places?
c)00111101 became 11101000. Which shift was applied, and by how many places?
An 8-bit value is shifted three places left and no 1 bit is discarded. What happens to its denary value?
- AIt is multiplied by 8
- BIt is multiplied by 3
- CIt is divided by 8
- DIt stays the same
4. File-size methods
Write the formula first, substitute values, calculate, then convert units if asked.
Image size in bits = width × height × colour depth
Sound size in bits = sample rate × bit depth × duration in seconds
Use the units provided by the question. In these tasks, use 8 bits = 1 byte, 1000 bytes = 1 KB and 1000 KB = 1 MB. OCR questions will state or imply the conversion convention required.
For a collection of files, calculate one file and then multiply by the number of files. A common mistake is to complete the first part and forget this final multiplication.
An uncompressed exhibition image is 800 pixels wide and 600 pixels high with a colour depth of 8 bits. Calculate its file size in bytes. Show your working. (3 marks)
Write the image formula, calculate the number of bits, then divide by 8.
Students type their answer here.
The exhibition stores 12 uncompressed sound clips. Each has a sample rate of 20,000 Hz, a bit depth of 8 bits and a duration of 5 seconds. Calculate the total size of all 12 clips in KB using 1000 bytes = 1 KB. Show your working. (5 marks)
Calculate one clip in bits, convert to bytes and KB, then multiply by 12. Label the final unit.
Students type their answer here.
A student increases the colour depth of an image but keeps its dimensions unchanged. What is the direct effect on the uncompressed file size?
- AIt decreases because the image has fewer pixels
- BIt increases because more bits are stored for each pixel
- CIt stays identical because the width is unchanged
- DIt becomes a sound file
5. Check the answer
A reliable check asks:
- Did every value from the question appear in my working?
- Are the units consistent at each step?
- Did I multiply or divide in the correct direction when converting units?
- If quality settings increased, did the uncompressed size also increase?
The next task includes a plausible-looking error.
A student calculates a 1000 × 500 pixel image at 16-bit colour depth as 8,000,000 bytes. Identify the error and give the correct file size in bytes. (3 marks)
Recalculate the size in bits, then identify the missing conversion.
Students type their answer here.
Challenge: A gallery must halve the uncompressed size of each sound clip without changing its duration. Explain one setting change that would achieve this and one effect on quality. (3 marks)
Choose sample rate or bit depth. State a precise change and its consequence.
Students type their answer here.
Finish: method marks are visible thinking
Do not hide a calculation in your head. A formula, substituted values, intermediate result and labelled final unit make your reasoning easy to reward and easy to debug.