Cambridge Syllabus Notes

📦 Data Storage & Compression

In IGCSE Computer Science, you’ll need to know how to measure how much data a file or a set of files takes up, and how to make that data smaller with compression. Think of data as a library: the more books you have, the more shelves you need. Storage units are the shelves, and compression is like putting books into a tighter stack.

🔢 Bits and Bytes

Everything in a computer is stored as bits (0 or 1). A byte is 8 bits.

$$1 \text{ byte} = 8 \text{ bits}$$

When you see a file size like 5 MB, it means 5 megabytes of data.

📊 Units of Storage

Unit	Abbreviation	How many of the previous unit?
Byte	B	1
Kilobyte	KB	$2^{10}=1024$
Megabyte	MB	$2^{10}$ KB
Gigabyte	GB	$2^{10}$ MB
Terabyte	TB	$2^{10}$ GB
Petabyte	PB	$2^{10}$ TB

Remember: 1 KB = 1024 B, 1 MB = 1024 KB, and so on.

🔄 Converting Units

To increase a unit (e.g., KB to MB), multiply by 1024.
To decrease a unit (e.g., GB to MB), divide by 1024.

Example: 5 GB to bytes:

$$5 \times 1024^3 = 5 \times 1\,073\,741\,824 = 5\,368\,709\,120 \text{ bytes}$$

🧩 Compression Basics

Compression reduces the size of data so it takes up less storage or bandwidth.

Lossless compression keeps every bit of data. Example: ZIP, PNG.
Lossy compression removes some data to achieve higher compression. Example: JPEG, MP3.

Analogy: Lossless is like folding a letter neatly – you can unfold it exactly as it was. Lossy is like compressing a photo with a filter – some details are lost but the image still looks good.

📐 Compression Ratio

The compression ratio tells you how much smaller the compressed file is compared to the original.

Formula: Compression ratio = $\frac{\text{original size}}{\text{compressed size}}$

Example: A 10 MB file compressed to 2 MB:

$$\frac{10}{2} = 5$$

So the ratio is 5:1 – the compressed file is 5 times smaller.

📚 Exam Tips

Always use 1024 when converting between binary units (KB, MB, GB, etc.).
Show your work when converting units or calculating compression ratios.
Remember: 1 KB = 1024 B, 1 MB = 1024 KB, 1 GB = 1024 MB.
When asked to calculate storage for a set of files, sum the sizes first before converting.
For compression questions, identify whether the method is lossless or lossy and give an example.
Use the formula for compression ratio: original / compressed and express the answer as a ratio (e.g., 4:1).
When converting to bytes, use bytes = kilobytes × 1024, then repeat for higher units.
Use a calculator for large numbers, but show the multiplication steps.
Check that your final answer is in the correct unit requested by the question.
Remember that exam questions may ask you to convert petabytes to gigabytes or vice versa – use the table for quick reference.

Understand how data storage is measured