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S4 ICT: Data Representation and Binary Encoding (Paper 3 (challenge))
Tutor Prep Guide · data representation: binary and hexadecimal conversion, bits and bytes, two’s complement and sign-magnitude, character encoding (ASCII and Unicode), bitmap image and sampled sound size, lossy versus lossless compression
S4 ICT: Data Representation and Binary Encoding (Paper 3 (challenge))
Paper 3 (challenge): ten data representation questions with answers and one-line notes.
Direct answers Level: S4 ICT; format: number base conversion, bits and bytes, two’s complement, character encoding, image and sound size, compression.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S4 ICT: Data Representation and Binary Encoding |
| Level | S4 |
02 Questions (10 items)
- FoundationA 1 920 by 1 080 image at 24 bits per pixel is stored uncompressed. What is its size in bytes and MiB?
- FoundationStereo audio at 44.1 kHz and 16 bits runs for three minutes. What is the uncompressed size in bytes and MiB?
- FoundationA 4 MiB file is compressed at a ratio of 8 to 1. What is the compressed size?
- IntermediateAdd hexadecimal 1F and 21, giving both hex and denary answers.
- IntermediateWork out 5 minus 9 in 8-bit two’s complement.
- IntermediateHow many bits per pixel are needed to show 256 colours?
- ChallengeAn uncompressed video clip is 640 by 480 at 24-bit colour, 25 frames per second, lasting 10 seconds. Give bytes and MiB.
- ChallengeEncode the string AAAABBBCCD with run-length encoding: how many characters result, and what percentage is saved?
- ChallengeHow many samples are captured in five minutes at 44.1 kHz?
- Error redoA student claims binary 0.1 equals denary 0.1. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 6 220 800 bytes, about 5.93 MiB | 1 920 times 1 080 times three bytes gives 6 220 800, and dividing by 1 048 576 gives 5.93. |
| 2 | 31 752 000 bytes, about 30.28 MiB | 44 100 samples times two bytes times two channels times 180 seconds gives 31 752 000. |
| 3 | 0.5 MiB | Four divided by eight gives 0.5, since the ratio compares original size to compressed size. |
| 4 | 40, which is 64 | 31 plus 33 is 64, and 64 equals four sixteens plus zero, written 40. |
| 5 | 11111100, which is minus four | Adding five and minus nine leaves 252, and after dropping the carry it reads as minus four. |
| 6 | 8 bits | Two to the eighth power is 256, so eight-bit colour depth is enough. |
| 7 | 230 400 000 bytes, about 219.73 MiB | 640 times 480 times three bytes times 25 frames times ten seconds gives 230 400 000. |
| 8 | 4A3B2C1D, eight characters, saving 20 percent | Ten characters shrink to eight, and the two saved over ten gives 20 percent. |
| 9 | 13 230 000 samples | 44 100 samples per second times 300 seconds gives 13 230 000. |
| 10 | Binary 0.1 is one half, that is 0.5, because the fractional weights are a half, a quarter and an eighth | Each weight halves, so 0.1 is 0.5 and 0.11 is 0.75. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
A computer only knows 0 and 1, so text, images and sound are all encoded into bits first. Keep bits apart from bytes, remember the top bit of a two’s complement number is a negative weight, and compute image or sound size as count times bits per item divided by eight, then check the unit in bytes, KiB or MiB.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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