CS17: Units of Information
Understanding bits, bytes, and larger units; calculating file sizes; and comparing data quantities.
📋 Fundamental Units
A bit (binary digit) is the smallest unit of data in computing. It can hold exactly one of two values: 0 or 1. All data in a computer - text, images, sound, video - is ultimately stored as bits.
| Unit | Size | What It Can Store |
|---|---|---|
| Bit | 0 or 1 | A single binary digit: on/off, yes/no, true/false |
| Byte | 8 bits | A single character (in ASCII), a number from 0-255 |
| Nibble | 4 bits | A single hex digit (0-F) |
Key Relationships:
1 nibble = 4 bits = 1 hex digit
1 byte = 8 bits = 2 nibbles = 2 hex digits
1 byte can represent 2^8 = 256 different values (0-255)
1 nibble = 4 bits = 1 hex digit
1 byte = 8 bits = 2 nibbles = 2 hex digits
1 byte can represent 2^8 = 256 different values (0-255)
📊 Larger Units
Larger units are multiples of bytes. At GCSE, you need to know the standard SI prefixes. Note: some specifications use powers of 2 (KiB, MiB) but most GCSE exams use the decimal (power of 10) definitions.
| Unit | Size (Decimal) | Equivalent |
|---|---|---|
| Kilobyte (KB) | 1,000 bytes | 10^3 bytes |
| Megabyte (MB) | 1,000,000 bytes | 10^6 bytes / 1,000 KB |
| Gigabyte (GB) | 1,000,000,000 bytes | 10^9 bytes / 1,000 MB |
| Terabyte (TB) | 1,000,000,000,000 bytes | 10^12 bytes / 1,000 GB |
| Petabyte (PB) | 1,000,000,000,000,000 bytes | 10^15 bytes / 1,000 TB |
Converting Between Units:
To go UP (e.g. bytes to KB): divide by 1,000
To go DOWN (e.g. KB to bytes): multiply by 1,000
5,000 bytes = 5,000 / 1,000 = 5 KB
3 MB = 3 x 1,000 x 1,000 = 3,000,000 bytes
To go UP (e.g. bytes to KB): divide by 1,000
To go DOWN (e.g. KB to bytes): multiply by 1,000
5,000 bytes = 5,000 / 1,000 = 5 KB
3 MB = 3 x 1,000 x 1,000 = 3,000,000 bytes
Note on binary prefixes: Some systems use KiB (kibibyte = 1024 bytes), MiB (mebibyte = 1048576 bytes), etc. These use powers of 2 (2^10 = 1024). Check your exam board specification for which system to use. Most GCSE exams use the decimal (1000-based) system.
💾 Calculating File Sizes
To calculate file sizes, you need to know how many bits or bytes are needed to store each element, then multiply by the number of elements.
Text File Size
Calculating Text File Size
If each character is stored using 1 byte (ASCII):
File size (bytes) = number of characters x 1
A text with 500 characters = 500 bytes
A text with 3,000 characters = 3,000 bytes = 3 KB
Image File Size
Calculating Bitmap Image Size
Image size (bits) = width x height x colour depth
A 1920x1080 image with 24-bit colour:
Size = 1920 x 1080 x 24
= 49,766,400 bits
= 6,220,800 bytes
= 6,220.8 KB
= 6.22 MB
Sound File Size
Calculating Sound File Size
File size (bits) = sample rate x sample resolution x duration (seconds)
A 3-minute song recorded at 44,100 Hz with 16-bit samples:
Size = 44,100 x 16 x 180
= 127,008,000 bits
= 15,876,000 bytes
= 15,876 KB
= 15.876 MB
For stereo (2 channels): multiply by 2 = 31.75 MB
⚖️ Comparing Quantities
When comparing data quantities, always convert both values to the same unit first. This avoids confusion and makes comparison straightforward.
Comparing File Sizes
Which is larger: 2,500 KB or 2 MB?
2 MB = 2 x 1,000 KB = 2,000 KB 2,500 KB > 2,000 KB So 2,500 KB is larger than 2 MB
Storage Capacity Comparison
| Item | Approximate Size |
|---|---|
| A text message | ~100 bytes |
| A word document (10 pages) | ~50 KB |
| A photo from a phone camera | ~3-5 MB |
| A song (MP3) | ~3-5 MB |
| A HD movie | ~2-4 GB |
| A hard drive | ~1-4 TB |
⚠️ Common Mistakes
| Mistake | Why It's Wrong | How to Fix It |
|---|---|---|
| Confusing bits and bytes | 1 byte = 8 bits, so 100 bytes = 800 bits | Always check whether the question asks for bits or bytes |
| Using 1024 instead of 1000 | GCSE typically uses decimal (1000-based) units | Check your exam board - most use 1000 for KB, MB, GB |
| Forgetting to convert units before comparing | 2 MB vs 1500 KB cannot be compared directly | Convert both to the same unit first |
| Not including colour depth for images | Size = width x height is missing the colour depth | Image size = width x height x colour depth |
| Forgetting channels for sound | Stereo has 2 channels, mono has 1 | Multiply by number of channels for stereo sound |
❓ Practice Questions
Q1: How many bytes are in 3.5 KB?
Q2: A text file contains 2,000 characters stored in ASCII (1 byte per character). What is the file size in KB?
Q3: Calculate the size of a 640x480 pixel image with 8-bit colour depth in KB.
Q4: Which is larger: 0.5 GB or 600 MB? Show your working.
Q5: A sound file is recorded at 22,050 Hz with 8-bit samples for 60 seconds. Calculate the file size in MB.
✅ Answers
- 3.5 KB = 3.5 x 1,000 = 3,500 bytes.
- 2,000 characters x 1 byte = 2,000 bytes = 2,000 / 1,000 = 2 KB.
- 640 x 480 x 8 = 2,457,600 bits = 307,200 bytes = 307.2 KB.
- 0.5 GB = 0.5 x 1,000 = 500 MB. 600 MB > 500 MB, so 600 MB is larger.
- 22,050 x 8 x 60 = 10,584,000 bits = 1,323,000 bytes = 1,323 KB = 1.323 MB.
🎯 Exam Tips
- 1 byte = 8 bits - this is the most fundamental relationship to remember
- For GCSE, typically use 1000 (not 1024) as the multiplier between units
- Always convert to the same unit before comparing
- For image size: width x height x colour depth (in bits)
- For sound size: sample rate x resolution x duration x channels
- Check if the question asks for the answer in bits, bytes, KB, or MB
⚠️ Common Errors
✗ Confusing bits and bytes ✓ 1 byte = 8 bits. A bit is a single 0 or 1; a byte is the smallest addressable unit of memory and can store one character.
✗ Thinking 1 KB = 1000 bytes ✓ In computing, 1 KiB (kibibyte) = 1024 bytes (2¹⁰). The term KB is often used informally for 1024 bytes, though technically KB = 1000 bytes in SI units.
✗ Mixing up the prefixes: kilo, mega, giga, tera ✓ Each prefix is 1024 times the previous: 1 KiB = 1024 B, 1 MiB = 1024 KiB, 1 GiB = 1024 MiB, 1 TiB = 1024 GiB.
✗ Forgetting that file sizes and storage are measured in bytes, not bits ✓ Storage and file sizes use bytes (KB, MB, GB). Network speeds are often measured in bits per second (Mbps, Gbps). Don't confuse MB with Mb.
✍️ Model Answer
Full-Mark Response
A photo is 4.2 MB. Calculate how many photos of this size can be stored on a 16 GB memory card. Show your working and state any assumptions. [3 marks]
16 GB = 16 × 1024 MB = 16384 MB Number of photos = 16384 ÷ 4.2 = 3900.95... Assumption: 1 GB = 1024 MB (binary prefix) and the storage has no overhead for file system metadata. Approximately 3900 photos can be stored.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Computational Thinking — 40%): Demonstrate knowledge and understanding of the principles and concepts of computer science, including units of information: bits, bytes and prefixes for AQA 8525, OCR J277 & Edexcel 1CP2.
AO2 (Application — 40%): Apply knowledge and understanding of computer science, including units of information: bits, bytes and prefixes to analyse problems in computational terms and to design, write and evaluate solutions.
AO3 (Evaluation — 20%): Evaluate the effectiveness, correctness and efficiency of computational solutions, including units of information: bits, bytes and prefixes, and make reasoned judgements about trade-offs.
📝 Exam Technique
GCSE Computer Science Exam Tips:
Know the hierarchy: bit → byte → KiB → MiB → GiB → TiB. Each step is ×1024. Always convert to the same unit before calculating. Watch for bits vs bytes (b vs B). If a question asks about storage capacity, convert everything to the same unit first. Show your conversion steps clearly for method marks.
Know the hierarchy: bit → byte → KiB → MiB → GiB → TiB. Each step is ×1024. Always convert to the same unit before calculating. Watch for bits vs bytes (b vs B). If a question asks about storage capacity, convert everything to the same unit first. Show your conversion steps clearly for method marks.
📝 Exam Questions by Topic
- AQA Past Papers - Topic Questions -- AQA
- Edexcel Past Papers - Topic Questions -- Edexcel
- OCR Past Papers - Topic Questions -- OCR
- Eduqas Past Papers - Topic Questions -- Eduqas
🎬 Video Resources
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