Units of information
Computers measure data and storage in bits and bytes, then in standardised multiples (kilobyte, megabyte, gigabyte, terabyte). AQA's spec uses the 1024 (binary) prefix convention rather than the SI 1000 convention. Read the question carefully — both turn up.
Base units
- Bit (b): the smallest unit — a single 0 or 1.
- Nibble: 4 bits.
- Byte B: 8 bits — enough to store one ASCII character.
The capital matters: B = byte, lowercase b = bit. A 100 Mbps internet connection = 100 megabits per second; a 100 MB file = 100 megabytes. Multiplying or dividing by 8 connects the two.
AQA's 1024 multiples
AQA uses powers of 1024 (= 2¹⁰):
| Unit | Symbol | Bytes | Approx |
|---|---|---|---|
| Kilobyte | KB | 1,024 | ~1,000 (10³) |
| Megabyte | MB | 1,024 × 1,024 | ~10⁶ |
| Gigabyte | GB | 1,024³ | ~10⁹ |
| Terabyte | TB | 1,024⁴ | ~10¹² |
So 1 KB = 1,024 B; 1 MB = 1,024 KB = 1,048,576 B; etc.
Converting between units
To go up a unit (e.g. KB → MB), divide by 1024. To go down a unit (e.g. MB → KB), multiply by 1024.
Worked example: convert 5,120 KB to MB. 5,120 ÷ 1024 = 5 MB.
Worked example: convert 2 GB to bytes. 2 × 1024³ = 2 × 1,073,741,824 = 2,147,483,648 B.
SI vs binary (the 1000 vs 1024 confusion)
In real life:
- Hard drive manufacturers use SI prefixes (1 TB = 10¹² bytes = 1,000,000,000,000 B). That's why a "1 TB" drive shows up as ~931 GiB in your OS.
- RAM and binary file sizes typically use 1024-multiples.
The IEC introduced KiB, MiB, GiB, TiB (kibi-, mebi-, gibi-, tebi-) for the 1024 versions. AQA still uses KB/MB/GB to mean 1024-based — so for exams, stick with 1024.
File-size calculations
A common exam pattern: estimate file sizes.
- Image: width × height × bits-per-pixel ÷ 8 → bytes.
- Sound: sample rate × duration × bit depth ÷ 8 → bytes.
- Text: number of characters × bits-per-character ÷ 8 → bytes.
Example: a 1024×768 image with 24-bit colour. 1024 × 768 × 24 ÷ 8 = 2,359,296 bytes = 2,359,296 ÷ 1024 = 2304 KB = 2304 ÷ 1024 = 2.25 MB.
✦Worked example— Worked example — character text file
A text file contains 50,000 ASCII characters (1 byte per character). What is its size in KB?
50,000 ÷ 1024 ≈ 48.83 KB.
✦Worked example— Worked example — bandwidth vs storage
You download an 8 MB file at 4 Mbps (megabits per second). How long does it take?
8 MB = 64 Mb (× 8). At 4 Mbps, it takes 64 ÷ 4 = 16 seconds.
⚠Common mistakes— Pitfalls
- Confusing bits with bytes. 1 byte = 8 bits — the factor of 8 trips up download-time questions.
- Wrong direction. Going from bytes to KB you divide by 1024, not multiply.
- Mixing 1000 and 1024. Stick with one convention per question — AQA prefers 1024.
- Forgetting to convert pixel counts.
width × heightgives pixels; multiply by bits-per-pixel and divide by 8 for bytes. - Ignoring the prefix difference: Mb vs MB. Lowercase b = bits, uppercase B = bytes.
➜Try this— Quick check
A USB stick has 16 GB (using 1024 prefix). How many bytes is that? 16 × 1024³ = 16 × 1,073,741,824 = 17,179,869,184 bytes ≈ 17.2 billion bytes.
AI-generated · claude-opus-4-7 · v3-deep-computer-science