Fitting the Prize-Day Gallery onto a 4 GB Card
The ICT club of a school has been asked to prepare a digital photo gallery for the annual prize day. A parent has donated a 4 GB SD card, and the club must decide whether the whole gallery fits on it. The club plans to include 600 photographs, each captured at 3000 x 2000 pixels with 24-bit colour. The card's capacity is stated using the manufacturer's decimal convention (1 GB = 1 000 000 000 bytes), while the club's file manager reports capacity in GiB (1 GiB = 1 073 741 824 bytes). The club also wants to add a three-minute narration recorded at 44 100 Hz, 16-bit, stereo, and to keep the photographs in a format that a projector can display without a computer. One member suggests simply reducing colour depth to 16 bits instead of compressing the images.
1. Calculate the size of one uncompressed photograph and of all 600 photographs, and decide whether the gallery fits on the donated card as uncompressed files. Show all working in bytes, then in GB.
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One image
- Pixels = 3000 x 2000 = 6 000 000
- 24-bit colour = 3 bytes per pixel
- 6 000 000 x 3 = 18 000 000 bytes (about 18 MB decimal, 17.2 MiB)
600 images
- 18 000 000 x 600 = 10 800 000 000 bytes = 10.8 GB
Compare with the card
- Card = 4 000 000 000 bytes (which the file manager shows as about 3.73 GiB, not 4 GiB)
- 10.8 GB is roughly 2.7 times the card's real capacity, so the gallery does not fit uncompressed.
Examiner point: the conclusion must be based on the decimal byte figure the manufacturer quotes, not on 4 x 1 073 741 824. Using the binary figure gives 4.29 GB, which still does not change the answer, but the working shows whether the candidate understands why the card 'looks smaller' in the file manager.
2. The club saves the photographs as JPEG at an 8:1 compression ratio and keeps the narration as uncompressed WAV. Calculate the new total size and decide whether everything now fits, leaving a sensible safety margin.
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Photographs after compression
- 10 800 000 000 / 8 = 1 350 000 000 bytes = 1.35 GB
Narration (uncompressed)
- 44 100 samples per second x 2 bytes x 2 channels = 176 400 bytes per second
- 176 400 x 180 s = 31 752 000 bytes, about 31.8 MB
Total
- 1 350 000 000 + 31 752 000 = 1 381 752 000 bytes, about 1.38 GB
- Card capacity 4 000 000 000 bytes, so roughly 2.6 GB remains
Judgement It fits comfortably, and it would still fit even at a 4:1 ratio (2.7 GB). Two cautions belong in the answer: JPEG is lossy, so one sample should be converted and checked on the actual projector before batch-converting all 600; and the originals must be kept elsewhere, because compression cannot be undone. The narration would also be far smaller as MP3, which would free further space if more photographs were added later.
3. A club member argues that reducing colour depth to 16 bits is better than compressing, because 'nothing is lost'. Evaluate this suggestion using calculations.
Read the worked answer
Recalculate at 16-bit colour
- 2 bytes per pixel x 6 000 000 = 12 000 000 bytes per image (12 MB)
- 12 000 000 x 600 = 7 200 000 000 bytes = 7.2 GB
Verdict: it does not solve the problem. 7.2 GB still exceeds the 4 GB card. Moving from 24-bit to 16-bit removes only one third of the data, but the club needs to remove about 63 % (from 10.8 GB down to below 4 GB).
Second flaw in the argument: the claim that 'nothing is lost' is false. 16 bits gives 65 536 colours per pixel instead of 16.7 million, which produces visible banding in skies and skin tones, and screens and projectors display 24-bit colour, so the loss is real and visible.
Conclusion: compression is the right lever because photographic data is highly redundant, so an 8:1 JPEG reduces size by a factor of eight while remaining visually acceptable. Reducing resolution (for example to 1500 x 1000) would be a second valid lever if more space were ever needed.