What You'll Learn
Binary Data
Why computers store everything as 0s and 1s
Units of Storage
From bits to petabytes - measuring data
Unit Conversion
Converting between different data units
File Size Calculations
Calculate sizes for images, sound, and text
Why Computers Use Binary
Everything is Binary
Computers can only understand two states: ON (1) or OFF (0). This is called binary.
All data - text, images, videos, music, games - must be converted to binary (0s and 1s) before a computer can process, store, or transmit it.
Why Binary Works
- Simple circuits - Easy to build with transistors (on/off switches)
- Reliable - Only 2 states means less chance of errors
- Fast switching - Transistors can switch billions of times per second
- Universal - Any data can be represented as numbers
Real-World Analogy
Think of Morse code - it uses just dots and dashes to represent any message. Binary is similar, but uses 0s and 1s instead.
Units of Data Storage
Data is measured in specific units. The smallest unit is a bit, and we group bits together to make larger, more practical units.
| Unit | Symbol | Size | Example Use |
|---|---|---|---|
| Bit | b | Single 0 or 1 | The smallest unit of data |
| Nibble | - | 4 bits | One hexadecimal digit (0-F) |
| Byte | B | 8 bits | One character (letter, number, symbol) |
| Kilobyte | KB | 1,000 bytes | A short email or text document |
| Megabyte | MB | 1,000 KB | An MP3 song (3-5 MB) |
| Gigabyte | GB | 1,000 MB | A movie or large game |
| Terabyte | TB | 1,000 GB | Hard drive capacity |
| Petabyte | PB | 1,000 TB | Data centres, cloud storage |
Key Pattern
Each unit is 1,000 times larger than the previous one (using decimal/SI units).
Note: Some systems use 1,024 (binary) instead of 1,000. Both are acceptable in exams.
Visualising Data Units
Converting Between Units
Going UP (smaller to larger)
Divide by 1,000
5,000 KB ÷ 1,000 = 5 MB
2,500,000 bytes ÷ 1,000 ÷ 1,000 = 2.5 MB
Going DOWN (larger to smaller)
Multiply by 1,000
3 GB × 1,000 = 3,000 MB
1.5 TB × 1,000 × 1,000 = 1,500,000 MB
Try It: Unit Converter
Calculating File Sizes
You need to know how to calculate the file size for different types of data. Each type has its own formula.
Image File Size
- 1 bit = 2 colours (black & white)
- 8 bits = 256 colours
- 24 bits = 16.7 million colours (true colour)
- 32 bits = 16.7 million colours + transparency
Example: Calculate the file size of an image
An image is 1920 × 1080 pixels with 24-bit colour depth.
Sound File Size
- 8,000 Hz = Phone quality
- 44,100 Hz = CD quality
- 48,000 Hz = DVD/professional quality
- 8-bit = Basic quality
- 16-bit = CD quality
- 24-bit = Professional quality
Example: Calculate the file size of an audio clip
A 3-minute stereo audio clip at CD quality (44,100 Hz, 16-bit).
Text File Size
- ASCII = 7 or 8 bits (128 or 256 characters)
- Unicode (UTF-8) = 8-32 bits (supports all languages)
- Common assumption: 8 bits (1 byte) per character
Example: Calculate the file size of a text document
A document contains 5,000 characters using ASCII encoding (8 bits per character).
Calculating Storage Requirements
When planning storage, you need to calculate the total capacity required for all your files.
Example: Planning a photo storage device
A photographer needs to store 500 photos. Each photo is 4000 × 3000 pixels with 24-bit colour.
Exam Tips
- Always show your working - you get marks for method even if the final answer is wrong
- Convert to the unit asked for in the question
- Remember: 8 bits = 1 byte (divide by 8 to go from bits to bytes)
- Use 1,000 for conversions (or 1,024 if specified)
- Don't forget stereo = ×2 for audio files
Quick Reference
Unit Conversions
- 8 bits = 1 byte
- 1,000 bytes = 1 KB
- 1,000 KB = 1 MB
- 1,000 MB = 1 GB
- 1,000 GB = 1 TB
- 1,000 TB = 1 PB
File Size Formulas
- Image: W × H × colour depth
- Sound: sample rate × duration × bit depth
- Text: characters × bits per char
Common Values
- CD audio: 44,100 Hz, 16-bit
- True colour: 24-bit depth
- ASCII text: 8 bits/char
- HD image: 1920 × 1080