Data Representation Exam Practice

This lesson brings together all the key topics from the Data Representation unit and provides exam-style questions with model answers. Use this lesson to test your understanding and practise the types of questions you will face in the GCSE Computer Science exam.

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Topic Checklist

Before tackling exam questions, make sure you are confident with all of these topics:

• Converting between binary, denary, and hexadecimal
• Binary addition and overflow errors
• Binary shifts (left and right)
• ASCII and Unicode character encoding
• Representing images (resolution, colour depth, file size)
• Representing sound (sample rate, bit depth, file size)
• Units of data storage and conversions
• Lossy and lossless compression (including RLE)

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Exam-Style Questions with Model Answers

Question 1: Number Conversion (3 marks)

Convert the denary number 178 to an 8-bit binary number. Show your working.

Model Answer:

128	64	32	16	8	4	2	1
1	0	1	1	0	0	1	0

• 178 ≥ 128 → 1, remainder 50
• 50 < 64 → 0
• 50 ≥ 32 → 1, remainder 18
• 18 ≥ 16 → 1, remainder 2
• 2 < 8 → 0
• 2 < 4 → 0
• 2 ≥ 2 → 1, remainder 0
• 0 < 1 → 0

178 in binary = 10110010

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Question 2: Binary Addition (3 marks)

Add the following two 8-bit binary numbers: 01101010 + 01010111. State any issues with the result.

Model Answer:

  Carries:  1 1 1 1 1 1
            0 1 1 0 1 0 1 0   (106)
          + 0 1 0 1 0 1 1 1   (87)
          -------------------
            1 1 0 0 0 0 0 1   (193)

The result is 11000001 (193 in denary). No overflow has occurred because the result fits within 8 bits (the maximum for 8-bit unsigned is 255).

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Question 3: Hexadecimal Conversion (2 marks)

Convert the hexadecimal number B3 to denary.

Model Answer:

• B = 11 in denary
• 11 × 16 = 176
• 3 × 1 = 3
• 176 + 3 = 179

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Question 4: Character Encoding (3 marks)

Explain one advantage and one disadvantage of using Unicode instead of ASCII.

Model Answer:

Advantage: Unicode can represent characters from virtually all world languages (over 140,000 characters), while ASCII is limited to 128 (or 256 in extended ASCII). This makes Unicode suitable for international applications and multilingual text.

Disadvantage: Unicode uses more bits per character (up to 32 bits in UTF-32, compared to 7 or 8 bits for ASCII), resulting in larger file sizes for the same amount of text.

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Question 5: Image File Size (3 marks)

A bitmap image has a resolution of 1024 × 768 pixels and uses 24-bit colour. Calculate the file size in megabytes (MB). Show your working.

Model Answer:

• Total pixels = 1024 × 768 = 786,432 pixels
• File size in bits = 786,432 × 24 = 18,874,368 bits
• File size in bytes = 18,874,368 ÷ 8 = 2,359,296 bytes
• File size in KB = 2,359,296 ÷ 1024 = 2304 KB
• File size in MB = 2304 ÷ 1024 = 2.25 MB

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Question 6: Sound File Size (3 marks)

A stereo audio recording has a sample rate of 44,100 Hz, a bit depth of 16 bits, and lasts for 5 minutes. Calculate the file size in MB. Show your working.

Model Answer:

• Duration in seconds = 5 × 60 = 300 seconds
• File size in bits = 44,100 × 16 × 300 × 2 (stereo) = 423,360,000 bits
• File size in bytes = 423,360,000 ÷ 8 = 52,920,000 bytes
• File size in KB = 52,920,000 ÷ 1024 ≈ 51,679.69 KB
• File size in MB = 51,679.69 ÷ 1024 ≈ 50.47 MB

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Question 7: Compression (4 marks)

A music streaming service uses lossy compression for its audio files. Explain why lossy compression is appropriate in this context, and give one situation where lossless compression would be more appropriate.

Model Answer:

Lossy compression is appropriate for a music streaming service because:

1. It significantly reduces file sizes, allowing songs to be transmitted quickly over the internet and reducing bandwidth usage.
2. The quality loss from lossy compression (e.g. MP3 encoding) is usually imperceptible to the average listener, so the listening experience is not significantly affected.
3. Smaller files mean the service can store more songs and users can stream with less data usage.

Lossless compression would be more appropriate in a professional recording studio where audio engineers need to edit and mix tracks at the highest possible quality. Any loss of audio data during compression could affect the final product, so formats like FLAC or WAV are preferred to preserve every detail of the recording.

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Question 8: Run-Length Encoding (3 marks)

The following data represents a row of pixels in a simple image: WWWWWBBBWWWWWWBBBB. Encode this data using Run-Length Encoding (RLE).

Model Answer:

Count the consecutive repeating values:

• 5 × W
• 3 × B
• 6 × W
• 4 × B

RLE encoding: 5W 3B 6W 4B

The original data was 17 characters. The RLE encoding uses 8 characters (4 pairs), achieving compression.

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Question 9: Binary Shifts (2 marks)

Perform a left shift by 2 on the binary number 00001011. State the denary value before and after the shift.

Model Answer:

• Original: 00001011 = 8 + 2 + 1 = 11 in denary
• Left shift by 2: 00101100 = 32 + 8 + 4 = 44 in denary
• Check: 11 × 4 = 44. Correct!

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Question 10: Data Units (2 marks)

A file has a size of 3,145,728 bytes. Convert this to megabytes.

Model Answer:

• 3,145,728 ÷ 1024 = 3072 KB
• 3072 ÷ 1024 = 3 MB

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Exam Strategy at a Glance

flowchart TD
    A[Read question] --> B{Identify topic}
    B -->|Number| C[Convert: bin/den/hex]
    B -->|Image| D[width x height x depth]
    B -->|Sound| E[rate x depth x time x channels]
    B -->|Compression| F[Lossy or Lossless?]
    C --> G[Show working]
    D --> G
    E --> G
    F --> G
    G --> H[Check units]
    H --> I[Final answer]

Key Exam Tips

1. Show your working — method marks are available even if the final answer is wrong.
2. Check your answers by converting back or using an alternative method.
3. Use the correct units — always state whether your answer is in bits, bytes, KB, MB, etc.
4. Read the question carefully — note whether it asks for binary, denary, or hex, and how many bits/marks are available.
5. Remember key formulas:
   • Image file size = width × height × colour depth
   • Sound file size = sample rate × bit depth × duration (× channels)
   • Number of values representable by n bits = 2ⁿ
6. Know the difference between lossy and lossless compression and when to use each.
7. Be precise with definitions — e.g. "resolution is the number of pixels in an image" not just "how clear it is".

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Summary