Data Representation Exam Practice (OCR J277 Paper 1 Style)

This lesson provides exam-style practice for the Data Representation topic of OCR J277 Paper 1 (Computer Systems). Data representation questions are a staple of Paper 1 and test your ability to convert between number systems, calculate file sizes, and explain encoding and compression.

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What to Expect in the Exam

Question type	Typical marks	Skills tested
Number system conversions	1-3	Binary, denary, hex conversions
Binary addition	2-3	Adding two 8-bit numbers, identifying overflow
Binary shifts	2-3	Left/right shifts, stating effect on value
File size calculation (image)	3-4	Using width x height x colour depth formula
File size calculation (sound)	3-4	Using sample rate x bit depth x duration formula
ASCII/Unicode comparison	2-4	Explaining differences, advantages, disadvantages
Compression explanation	3-6	Lossy vs lossless, RLE, Huffman coding
Unit conversions	1-2	Converting between bits, bytes, KB, MB, etc.

mindmap
  root((Data Representation Paper 1))
    Number Systems
      Binary to Denary
      Denary to Binary
      Hex Conversions
    Arithmetic
      Binary Addition
      Logical Shifts
      Overflow
    Encoding
      ASCII
      Unicode
    File Sizes
      Image WxHxD
      Sound RxBxTxC
    Compression
      Lossy
      Lossless
      RLE
      Huffman
    Units
      Bit Byte KB MB GB

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Practice Question 1: Binary to Denary (1 mark)

Convert the binary number 11010110 to denary.

128 + 64 + 16 + 4 + 2 = 214

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Practice Question 2: Denary to Hexadecimal (2 marks)

Convert the denary number 189 to hexadecimal.

Method: Convert to binary first.

• 189 = 10111101
• Split: 1011 | 1101
• 1011 = B, 1101 = D

Answer: BD

Alternative: 189 / 16 = 11 remainder 13. 11 = B, 13 = D. Answer: BD

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Practice Question 3: Binary Addition (2 marks)

Add the binary numbers 01110101 and 00101110. State if overflow occurs.

Row	b8	b7	b6	b5	b4	b3	b2	b1	Decimal
Carry	1	1	1	1	1	1
	0	1	1	1	0	1	0	1	117
+	0	0	1	0	1	1	1	0	46
Sum	1	0	1	0	0	0	1	1	163

Answer: 10100011 (163). No overflow because the result fits in 8 bits.

OCR Exam Tip: Overflow occurs when a carry is generated from the most significant bit (leftmost). If both numbers start with 0 (positive) and the result starts with 1, check carefully — for unsigned integers, the result is valid as long as it fits in 8 bits.

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Practice Question 4: Binary Shift (2 marks)

Perform a logical left shift by 2 positions on the binary number 00010100 (20). State the new denary value.

Before: 00010100 (20) After: 01010000 (80)

The value has been multiplied by 4 (2^2). 20 x 4 = 80.

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Practice Question 5: Image File Size (3 marks)

A digital photograph has a resolution of 2048 x 1536 pixels and uses 24-bit colour depth. Calculate the file size in megabytes (MB).

Step	Calculation	Result
Total pixels	2048 x 1536	3,145,728
Total bits	3,145,728 x 24	75,497,472
Bytes	75,497,472 / 8	9,437,184
MB	9,437,184 / (1024 x 1024)	9.0 MB

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Practice Question 6: Sound File Size (3 marks)

A stereo audio recording is 5 minutes long with a sample rate of 44,100 Hz and a bit depth of 16 bits. Calculate the file size in MB.

Duration: 5 x 60 = 300 seconds

Step	Calculation	Result
Total bits	44,100 x 16 x 300 x 2	423,360,000
Bytes	423,360,000 / 8	52,920,000
MB	52,920,000 / (1024 x 1024)	50.47 MB

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Practice Question 7: ASCII vs Unicode (4 marks)

Explain two differences between ASCII and Unicode.

Point	ASCII	Unicode
Character set size	128 characters (7-bit) or 256 (8-bit extended)	Over 149,000 characters
Language support	Primarily English/Latin alphabet	All written languages worldwide, plus emoji
Storage per character	1 byte	1-4 bytes (UTF-8) or 2-4 bytes (UTF-16)
File size	Smaller	Larger for the same text

Sample answer: ASCII uses 7 or 8 bits per character and can represent up to 256 characters, which is sufficient for English but not for other languages. Unicode can represent over 149,000 characters from all world languages. However, Unicode files are generally larger because each character may require more bits to store.

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Practice Question 8: Compression (4 marks)

A photographer stores images on their website. Explain why they would use lossy compression rather than lossless compression.

Sample answer:

• Lossy compression (e.g., JPEG) reduces the image file size significantly, often by 80-90%, which means the web page loads faster for visitors (1 mark).
• Lossy compression removes fine details that the human eye is unlikely to notice in a photograph, so the visible quality remains acceptable (1 mark).
• Smaller files use less server storage and less bandwidth, reducing hosting costs (1 mark).
• Lossless compression (e.g., PNG) would result in much larger files, making the website slower to load (1 mark).

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Practice Question 9: Run-Length Encoding (3 marks)

The following data represents a row of pixels in a simple image: WWWWWBBBWWWWWWBBB

Encode this using RLE.

W appears 5 times, then B appears 3 times, then W appears 6 times, then B appears 3 times.

RLE: 5W 3B 6W 3B

Original: 17 characters. Compressed: 8 characters (4 pairs). Significant reduction.

OCR Exam Tip: When answering RLE questions, clearly show the count followed by the value for each run. State the original and compressed sizes to demonstrate the space saving.

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Exam Strategy Checklist

1. Show your formula before substituting values in calculation questions
2. Show all working — method marks are available even if the final answer is wrong
3. State units in your answer (bits, bytes, KB, MB)
4. Double-check conversions by converting back to the original system
5. Use correct terminology — bit depth (not colour bits), sample rate (not sampling speed)
6. For comparison questions, use a structured format (table or bullet points) to ensure you cover both sides

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Worked Example: A Multi-Part Mixed Question (Image, Sound, and Conversion)

Multi-part questions that combine several data representation skills appear regularly in OCR J277 Paper 1. Here is a fully worked example.

Question: A music streaming app stores a 3-minute stereo audio clip at a sample rate of 48,000 Hz with a bit depth of 16 bits. The app also stores a 1024 x 768 thumbnail image using 8-bit colour depth. The colour index uses hex codes. Answer the following:

(a) Calculate the uncompressed size of the audio clip in MB. (3 marks)

(b) Calculate the uncompressed size of the thumbnail image in KB. (3 marks)