Worked example · Computer Science · Year 10
DCF: Interacting and collaborating → Storing and sharing
A complete, secure Year 10 answer, annotated so you can see which success criterion each part meets. It is also the answer key. The headline figures: P2 is 4,800 KB; A1 is 225,000 KB (219.73 MB); the whole collection uncompressed is 18.37 GB, which does not fit in 15 GB; lossless masters take 10.79 GB; masters plus web copies take 13.49 GB, leaving 1.51 GB. The most common mistake is dividing by 1,000 instead of 1,024; the second is forgetting to divide bits by 8.
| Question | Answer |
|---|---|
| Bits in 1 nibble; bits in 1 byte | 4 bits; 8 bits |
| Bytes in 1 KB | 1,024 bytes |
| KB in 1 GB | 1,024 × 1,024 = 1,048,576 KB |
| Colours with an 8-bit colour depth | 28 = 256 |
The KB in a GB answer needs two steps of 1,024, not one. Evidences criterion 2.
| Item | Working (bits) | Bytes | KB | MB |
|---|---|---|---|---|
| P1 | 2,048 × 1,536 × 8 = 25,165,824 | 3,145,728 | 3,072 | 3.00 |
| P2 | 1,600 × 1,024 × 24 = 39,321,600 | 4,915,200 | 4,800 | 4.69 |
| P3 | 2,480 × 3,508 × 1 = 8,699,840 | 1,087,480 | 1,061.99 | 1.04 |
| P4 | 320 × 240 × 24 = 1,843,200 | 230,400 | 225 | 0.22 |
(e) At 1 bit each pixel can only be pure black or pure white, so faint pencil, faded ink and the shading of the paper disappear or turn into speckles. At 8 bits each pixel can be one of 256 shades of grey, so faint writing stays readable. The file becomes 8 times bigger: 8,495.94 KB, about 8.30 MB instead of 1.04 MB. For a handwritten record that may be the only copy, being able to read it matters more than saving 7 MB.
Every row shows the formula with the real numbers, then each unit in turn: ÷ 8 for bytes, ÷ 1,024 for KB, ÷ 1,024 for MB. Part (e) links colour depth to both quality and size and makes a judgement for this item. Evidences criteria 1 and 2.
| Item | Seconds | Working (bits) | Bytes | KB | MB |
|---|---|---|---|---|---|
| A1 | 40 × 60 = 2,400 | 48,000 × 16 × 2,400 = 1,843,200,000 | 230,400,000 | 225,000 | 219.73 |
| A2 | 3 × 60 = 180 | 44,100 × 16 × 180 = 127,008,000 | 15,876,000 | 15,503.91 | 15.14 |
| A3 | 10 × 60 = 600 | 8,000 × 8 × 600 = 38,400,000 | 4,800,000 | 4,687.5 | 4.58 |
(d) A3 has a lower sample rate (8,000 Hz instead of 48,000 Hz) and a lower bit depth (8 bits instead of 16). One minute of A3 is 468.75 KB against 5,625 KB for A1, 12 times smaller. With fewer samples each second, high sounds are lost and voices sound muffled, like a telephone. With fewer bits per sample, each measurement is rounded more roughly, so there is more hiss.
Minutes are changed to seconds before multiplying. Part (d) names both settings and explains the effect of each on the sound. Evidences criteria 1 and 2.
| File | Compression ratio | Reduction in size | Master, web or both? Why? |
|---|---|---|---|
| P2 as PNG | 4,800 ÷ 2,400 = 2 : 1 | 2,400 ÷ 4,800 × 100 = 50.0% | Master. Lossless, so every pixel of the scan can be recovered exactly. |
| P2 as JPEG | 4,800 ÷ 480 = 10 : 1 | 4,320 ÷ 4,800 × 100 = 90.0% | Web. It loads fast and nobody will notice the lost detail on a screen, but detail is gone for good. |
| A1 as FLAC | 225,000 ÷ 140,625 = 1.6 : 1 | 84,375 ÷ 225,000 × 100 = 37.5% | Master. Lossless, so a future volunteer can clean up the sound from the full recording. |
| A1 as MP3 | 225,000 ÷ 37,500 = 6 : 1 | 187,500 ÷ 225,000 × 100 = 83.3% | Web. Much quicker to stream on a phone; speech still sounds clear. |
Ratios are written as something : 1 and reductions use the amount saved divided by the original. Each choice is tied to what the copy is for: lossless where the original must survive, lossy where speed and size matter. Evidences criteria 3 and 4.
(a) Photos: 1,200 × 4,800 KB = 5,760,000 KB. Interviews: 60 × 225,000 KB = 13,500,000 KB. Total 19,260,000 KB ÷ 1,024 = 18,808.59 MB ÷ 1,024 = 18.37 GB. This is 3.37 GB more than 15 GB, so it will not fit uncompressed.
(b) PNG photos: 1,200 × 2,400 KB = 2,880,000 KB. FLAC interviews: 60 × 140,625 KB = 8,437,500 KB. Total 11,317,500 KB ÷ 1,024 ÷ 1,024 = 10.79 GB.
(c) JPEG photos: 1,200 × 480 KB = 576,000 KB. MP3 interviews: 60 × 37,500 KB = 2,250,000 KB. Total 2,826,000 KB = 2.70 GB. Masters and web copies together: 11,317,500 + 2,826,000 = 14,143,500 KB = 13.49 GB. That fits, with 15 − 13.49 = 1.51 GB left over.
(d) Gareth, save every master as a lossless file: PNG for scans and FLAC for interviews. That keeps every detail and still cuts the size from 18.37 GB to 10.79 GB. Make a JPEG and an MP3 of each item for the website, because they load quickly on a phone. Everything then fits in the 15 GB account with 1.51 GB spare. Copy the masters to the drive in the vestry as a second copy in a second place. Name files type_year_place_number, for example photo_1974_aberdare-park_0002.png, so any volunteer can find and sort them.
The totals are correct, the units are converted in two clear steps, and the plan uses the numbers to justify each choice. It covers compression, a second copy and a naming pattern, the file management techniques named in the success criteria. The plan is 92 words. Evidences criteria 1, 3, 4 and 5.