Calculate the file size of an image file and a sound file, using information given
📚 Data Storage & Compression – IGCSE 0478
Objective
Calculate the file size of an image file and a sound file using the given information.
📷 Image File Size
Think of an image as a photo frame made of tiny coloured squares called pixels. Each pixel stores colour information.
- Number of pixels = width × height.
- Each pixel uses a certain number of bits (colour depth). Common depths: 8‑bit (256 colours), 24‑bit (16 777 216 colours).
- File size in bits = pixels × bits per pixel.
- Convert bits to bytes: divide by 8.
- Convert bytes to kilobytes (KB) or megabytes (MB) as needed.
Example: 1920 × 1080 image, 24‑bit colour.
| Step | Calculation | Result |
|---|---|---|
| Pixels | 1920 × 1080 | 2 073 600 |
| Bits per pixel | 24 | 24 |
| File size (bits) | 2 073 600 × 24 | 49 766 400 |
| File size (bytes) | 49 766 400 ÷ 8 | 6 220 800 |
| File size (MB) | 6 220 800 ÷ 1 048 576 | ≈ 5.94 MB |
Exam Tip: Always remember bits → bytes (÷8) and bytes → KB (÷1024) or MB (÷1 048 576).
🎧 Sound File Size
Sound is like a tape that records vibrations. The amount of data depends on:
- Sample rate (samples per second) – e.g., 44.1 kHz.
- Bit depth (bits per sample) – e.g., 16‑bit.
- Number of channels – 1 for mono, 2 for stereo.
- Duration (seconds).
Formula: File size (bits) = sample rate × bit depth × channels × duration.
Example: 44.1 kHz, 16‑bit, stereo, 3 minutes (180 s).
| Parameter | Value | |
|---|---|---|
| Sample rate | 44 100 Hz | |
| Bit depth | 16 bits | |
| Channels | 2 (stereo) | |
| Duration | 180 s | |
| File size (bits) | 44 100 × 16 × 2 × 180 | 253 344 000 |
| File size (bytes) | 253 344 000 ÷ 8 | 31 668 000 |
| File size (MB) | 31 668 000 ÷ 1 048 576 | ≈ 30.2 MB |
Exam Tip: Write the full formula before plugging in numbers. Check units (Hz, bits, seconds) to avoid mistakes.
🔍 Compression Basics
Compression reduces file size by removing redundant or unnecessary data.
- Lossless: No data lost (e.g., PNG, FLAC). Useful when quality matters.
- Lossy: Some data discarded for smaller size (e.g., JPEG, MP3). Acceptable for images/sounds where perfect fidelity isn’t critical.
Typical compression ratios:
| Format | Compression Type | Typical Ratio |
|---|---|---|
| PNG | Lossless | ~2–5 × |
| JPEG | Lossy | ~10–20 × |
| FLAC | Lossless | ~2–3 × |
| MP3 | Lossy | ~10–12 × |
Exam Tip: When asked about compression, identify whether the format is lossless or lossy and give a typical compression ratio. Use the example ratios above as a quick reference.
💡 Quick Summary
- Image size = width × height × bits per pixel ÷ 8.
- Sound size = sample rate × bit depth × channels × duration ÷ 8.
- Always convert bits → bytes, then to KB/MB.
- Compression reduces size; lossless keeps all data, lossy removes some.
Final Exam Tip: Practice converting between units and applying the formulas. Remember the order of operations: multiply first, then divide. Good luck! 🚀
Revision
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