O Level Computer Science: Data Representation — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Data Representation revision notes

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Section A

1. State the number of bits in a nibble, a byte and a word (typical). [2]

2. List these units in ascending order: KB, TB, GB, MB, bit, byte. [2]

Section B

3. Convert:

(a) 11001110₂ to denary [2] (b) 173₁₀ to binary [2] (c) 9F₁₆ to denary [2]

4. Perform a logical left shift of 2 places on 00010110.

(a) State the result. [1] (b) State the effect on the denary value. [2] (c) Explain what happens if a left shift causes a 1 to be lost. [2]

5. Explain how characters are represented in a computer.

(a) State how many characters ASCII can represent and why. [2] (b) Explain two advantages of Unicode over ASCII. [4] (c) Explain why the code for “A” is 65 and deduce the code for “D”. [2]

6. A sound file is recorded for 30 seconds at a sample rate of 44 100 Hz with a sample resolution of 16 bits, in mono.

(a) Calculate the file size in megabytes. [4] (b) State two ways the file size could be reduced and the drawback of each. [4]

7. An 8-bit register holds the value 11111111 (255 in denary), and 00000001 (1) is added to it.

(a) Perform the addition and state the 8-bit result. [2] (b) Explain why this is described as an overflow error. [2]

8. A bitmap image is 200 pixels wide and 150 pixels high, with a colour depth of 8 bits per pixel.

(a) Calculate the file size in kilobytes. [3] (b) State one way the file size could be reduced, and the effect this has on image quality. [2] (c) State one advantage of storing this image as a vector graphic instead, and one situation where a vector graphic would be unsuitable. [2]

9. Run-length encoding is a lossless compression method.

(a) Describe how run-length encoding compresses data. [2] (b) Explain why run-length encoding can sometimes produce a larger file than the original, and give an example of the kind of data where this happens. [2]

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Answers

1. Nibble = 4 bits; byte = 8 bits [1]; a word is typically 32 or 64 bits [1].

2. bit, byte, KB, MB, GB, TB [2 — 1 mark if one is misplaced].

3. (a) 128 + 64 + 8 + 4 + 2 = 206 [1] [1]. (b) 10101101 [1] [1]. (c) 9 × 16 + 15 = 159 [1] [1].

4. (a) 01011000 [1]. (b) The value is multiplied by 4 — from 22 to 88 [1] [1]. (c) The bit is shifted out of the register and lost [1], so the value is no longer a correct multiplication — the result is wrong because the register cannot hold a number that large [1].

5. (a) 128 characters [1], because standard ASCII uses 7 bits and 2⁷ = 128 [1]. (b) Unicode uses more bits per character, so it can represent far more characters — over a million code points [1] [1]. This means it can represent a very wide range of the world’s writing systems, plus symbols and emoji, so text can be exchanged internationally without corruption [1]; it is also backwards compatible with ASCII for the first 128 characters [1]. (c) The character codes are allocated in sequence starting at 65 for “A” [1]; “D” is three places later, so its code is 68 [1].

6. (a) Bits = 44 100 × 16 × 30 [1] [1] = 21 168 000 bits [1]; ÷ 8 ÷ 1 000 000 = 2.65 MB [1]. (b) Reduce the sample rate — the file gets smaller but higher frequencies are lost and quality falls [1] [1]. Reduce the sample resolution to 8 bits — smaller file but less precise amplitude measurement, so more background noise and distortion [1] [1]. (Also accept: apply lossy compression, which loses data permanently.)

7. (a) 11111111 + 00000001 = 00000000 (with a carry out of the register) [1] [1]. (b) The true sum, 256, needs 9 bits but the register can only hold 8 [1], so the result is too large for the number of bits allocated and the stored value (0) is incorrect [1].

8. (a) file size = 200 × 150 × 8 [1] = 240 000 bits ÷ 8 = 30 000 bytes [1] = 30 KB [1]. (b) Reduce the colour depth (e.g. to 4 bits) — smaller file, but fewer colours can be represented, so the image quality falls [1] [1]. (c) Vector graphics scale without loss of quality and are usually smaller for line art [1]; they would be unsuitable for a photograph, which needs the pixel-level detail a bitmap captures [1].

9. (a) It replaces runs of identical, repeated values with a single value and a count of how many times it repeats [1], so repetitive data is stored far more compactly [1]. (b) On noisy or photographic data, where pixel values rarely repeat exactly, encoding each short “run” (value, count) can take more space than the original data [1] — for example, a photograph with continuously varying colours, unlike an image with large uniform blocks of colour [1].

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Where marks are usually lost

• Forgetting that a left shift of n multiplies by 2ⁿ, not by n.
• Saying ASCII uses 8 bits (extended ASCII does; standard ASCII uses 7).
• Not converting bits to bytes in file size calculations.
• Confusing sample rate with sample resolution when suggesting reductions.
• Forgetting that overflow means the true result needs more bits than the register holds, not simply that “the answer is wrong”.
• Assuming compression always reduces file size — run-length encoding can enlarge noisy or photographic data with few repeated runs.