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S4 ICT: Data Representation and Binary Encoding (Paper 4 (error clinic))
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 4 (error clinic))
Paper 4 (error clinic): 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)
- FoundationHow many bytes are there in 40 bits?
- FoundationWhat denary value is the two’s complement pattern 11111111, and why is it not 255?
- FoundationWhat denary values do the hex digits A and F stand for, and what is 0xFF?
- IntermediateAn 800 by 600 image at 24-bit colour holds how many bits and how many bytes?
- IntermediateMono sound at 44.1 kHz and 16 bits uses how many bytes per second?
- IntermediateHow many bytes are in 2 MiB?
- ChallengeWhat is the denary value of binary 0.11?
- ChallengeWhich of JPEG and PNG is lossy, and how do they differ after decompression?
- ChallengeBy how much do the ASCII codes of the capital letters D and A differ?
- Error redoA student says Unicode is merely a lengthened ASCII, so one Chinese character takes a single byte. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 5 bytes | Converting bits to bytes means dividing by eight. |
| 2 | Minus one; 255 only appears if the same bits are read as unsigned | The top bit weighs minus 128 and the seven remaining ones bring the total to minus one. |
| 3 | A is 10 and F is 15, so 0xFF is 255 | Fifteen sixteens plus fifteen gives 255, and two hex digits fill exactly eight bits. |
| 4 | 11 520 000 bits, which is 1 440 000 bytes | 800 times 600 times 24 gives 11 520 000 bits, and dividing by eight gives 1 440 000 bytes. |
| 5 | 88 200 bytes | 44 100 samples times two bytes gives 88 200. |
| 6 | 2 097 152 bytes | One MiB is 1 024 times 1 024 bytes, then doubled. |
| 7 | 0.75 | The first fractional place is one half and the second is one quarter. |
| 8 | JPEG is lossy and PNG is lossless, so a lossy file never returns to the exact original | Lossy compression discards detail for a smaller file, and repeated saving accumulates the loss. |
| 9 | 3 | Letters sit consecutively in the ASCII table, so 68 minus 65 gives 3. |
| 10 | Unicode gives every script a code point, and in UTF-8 a Chinese character usually needs three bytes, while ASCII covers only 128 characters | The encoding and the byte count are different questions: one code point is not one byte. |
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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