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S4 ICT: Data Representation and Binary Encoding (Paper 1 (basics))
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 1 (basics))
Paper 1 (basics): 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)
- FoundationConvert denary 13 into a 4-bit binary number.
- FoundationWhat is the denary value of binary 10110?
- FoundationWhat is the denary value of hexadecimal 2A?
- IntermediateHow many bits are there in 3 bytes?
- IntermediateHow many bits are in a nibble, and how many values can it hold?
- IntermediateWhat is the largest value an 8-bit unsigned integer can hold?
- ChallengeAdd binary 1011 and 0110, and give the denary result.
- ChallengeHow many bytes are in 1 KiB, and how does it differ from 1 kB?
- ChallengeWrite denary 47 in BCD (binary coded decimal).
- Error redoA student writes denary 255 as binary 1111111 (seven ones). What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1101 | 13 equals 8 + 4 + 1, so the 8, 4 and 1 columns are set. |
| 2 | 22 | 16 + 4 + 2 gives 22. |
| 3 | 42 | 2 times 16 plus 10 gives 42, since A stands for ten. |
| 4 | 24 bits | One byte is 8 bits, so 3 times 8 gives 24. |
| 5 | 4 bits, giving 16 values | Two to the power four is sixteen, running from 0000 to 1111. |
| 6 | 255 | Two to the power eight minus one is 255, written 1111 1111. |
| 7 | 10001, which is 17 | 11 plus 6 is 17, which needs a fifth bit after the carry. |
| 8 | 1 KiB is 1 024 bytes, while 1 kB usually means 1 000 bytes | In binary prefixes K means two to the tenth power, whereas the decimal prefix k means one thousand. |
| 9 | 0100 0111 | Each decimal digit gets its own four bits, so 4 becomes 0100 and 7 becomes 0111. |
| 10 | All eight bits must be one, giving 1111 1111, because seven ones only reach 127 | Dropping one bit halves the range, so the bit count must be checked. |
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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