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J277 1 Paper 1 calculations and working
Part 2 of 7 · J277 Paper 1 · Exam transition
Non-calculator Paper 1 practice with fixed number grids and visible calculation working.
Students will:
- convert between denary, eight-bit binary and hexadecimal
- show binary addition results and incoming carries
- apply and identify logical shifts
- calculate image and sound sizes with the requested units
- find and repair a calculation error
Inside: 6 text sections, 2 multiple-choice activities, 4 number activities, 4 written answers. 28 marks. Suggested time: 60–80 minutes. 2 diagrams.
Includes a teacher guide with sections, timings, misconceptions and repair routes.
Series: J277 Paper 1 · Exam transition, part 2 of 7.
Shared by Coding PathwayVerified teacher
- 16 cells
- About 65 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.
Calculations and working
Practise choosing a method, showing it clearly and checking the result. Work without a calculator. Use the scratch space to check native number tasks; carries have their own assessed row in the addition tasks.
1. Represent the same value
An eight-bit number uses the place values 128, 64, 32, 16, 8, 4, 2, 1. Split it into two four-bit nibbles to convert to hexadecimal. One nibble corresponds to one hex digit.
Include leading zeros when asked for eight-bit binary or two-digit hexadecimal: 00001010 and 0A represent the same value.
Complete the two missing representations in each row. Use eight-bit binary and two-digit hexadecimal.
a)Denary 66. Fill in the binary and hexadecimal.
b)Binary 11001001. Fill in the denary and hexadecimal.
c)Hexadecimal 3C. Fill in the denary and binary.
2. Show the carry
Add from right to left. 1 + 1 = 10: write 0 and carry 1 into the next column. With an incoming carry, 1 + 1 + 1 = 11: write 1 and carry 1.
The carry row records the carry entering each column. A zero or an empty unused box means no carry. This small example uses four bits; your practice uses eight.
Converting to denary can check the result, but it does not show binary carry working.
Add each pair of eight-bit numbers. Complete the result and carry rows.
a)Add these 8-bit binary numbers: 01011011 + 00100111.
b)Add these 8-bit binary numbers: 00110110 + 00011101.
3. Track the bits
A logical left shift moves bits left and inserts zeros on the right. A one-place shift doubles an unsigned value if no 1 bit is lost; three places multiply it by 8.
A logical right shift inserts zeros on the left. Bits shifted out are discarded. A right shift by one place gives the whole-number part after division by 2, so an odd value is not divided exactly.
For apply, write the new value. For identify, give the direction and number of places; writing only the new value does not answer that question.
Shift the value left by two places. Give the eight-bit result and its denary value.
Apply a logical shift left of 2 places to 00010110.
Identify the direction and number of places in each logical shift.
a)00111000 became 00000111. Which shift was applied, and by how many places?
b)00010101 became 10101000. Which shift was applied, and by how many places?
An unsigned value is shifted left three places without losing any 1 bits. Which calculation gives the new denary value?
- AOriginal value × 3
- BOriginal value ÷ 8
- COriginal value × 8
- DOriginal value + 3
4. Calculate, then label the unit
For these tasks, ignore metadata and use uncompressed files with one sound channel.
Image size in bits = width × height × colour depth
Sound size in bits = sample rate in Hz × bit depth × duration in seconds
Use 8 bits = 1 byte, 1000 bytes = 1 KB and 1000 KB = 1 MB throughout this worksheet. For a collection, include the number of files. Write enough working to show which values you used; a correct final answer alone may earn only the result mark.
An uncompressed image is 160 pixels wide and 100 pixels high, with a colour depth of 4 bits. Calculate its size in bytes, ignoring metadata. Show your working.
Students type their answer here.
A display stores five uncompressed sound clips. Each clip has one channel, a sample rate of 8000 Hz, a bit depth of 8 bits and a duration of 3 seconds. Calculate the total size of all five clips in KB. Use 8 bits = 1 byte and 1000 bytes = 1 KB. Ignore metadata and show your working.
Students type their answer here.
An image keeps the same width and height, but its colour depth doubles. What happens to its uncompressed size, ignoring metadata?
- AIt doubles because each pixel uses twice as many bits
- BIt halves because there are fewer pixels
- CIt is unchanged because the width stays the same
- DIt increases the number of pixels by two
5. Find the type of error
Check the unit, the number of files and the direction of conversion. A calculation can use every correct value and still label a number of bits as bytes.
For the final sound task, duration stays fixed. Sample rate controls how often amplitude is measured; bit depth controls how many amplitude values can be represented.
A student calculates the size of a 200 × 100 pixel image at 16-bit colour depth as 320,000 bytes. Ignoring metadata, explain the unit error and give the correct size in bytes.
Students type their answer here.
A sound clip must have half its original uncompressed size. Its duration and number of channels must stay unchanged. State one precise change to a recording setting that would achieve this, then explain one possible effect on playback quality.
Students type their answer here.
Review
Repair one error and try a fresh example from the relevant number or data-representation worksheet. Check whether the problem was the method, arithmetic, required format or unit.