Storage units step in 1024s rather than 1000s because computers work in binary, and $1024=2^{10}$ — a round number in binary even though it looks arbitrary in denary.

The -bi- units (kibibyte, mebibyte) were introduced to make this explicit, since 'kilobyte' had been used ambiguously for both 1000 and 1024 bytes. In this syllabus, use the 1024-based units unless told otherwise.

This is also why a hard drive advertised as $1\text{TB}$ shows up as roughly $931\text{GiB}$ once connected to a computer: drive manufacturers advertise using 1000-based units, while most operating systems display the 1024-based figure. No storage is actually missing — the same physical drive is simply being measured on two different scales.

Storage is also measured on a purely decimal scale, using the ordinary metric prefixes and powers of 1000 instead of 1024:

These names look almost identical to the -bi- units but are a different, smaller value at every step, since $1000<1024$. Some exam questions use kilobyte, megabyte, gigabyte and terabyte to mean the decimal (powers-of-1000) value directly, with no kibi/mebi/gibi/tebi form at all — so check whether a question gives you the definition it wants, and use exactly the multiplier it states.

Work through the units in order and show each step. Method marks are available even if one division goes wrong, and skipping steps forfeits them.

The first line is the one most often forgotten: the formula needs seconds, so minutes must be converted before anything else.

A rough sanity check helps too. A few minutes of CD-quality audio is tens of megabytes; a photograph is a few megabytes. An answer of $15$ bytes or $15$ gigabytes signals an error in the unit conversion.

Questions usually want the benefit tied to a consequence. 'It makes the file smaller' is the definition, not the reason.

Better: a smaller file takes less time to transmit over a network of a given bandwidth, and takes up less storage space so more files can be kept. Both name what is actually gained.

Putting real numbers on it makes the case concrete: uncompressed 4K video can require several hundred megabits per second to stream, far beyond what most home internet connections could sustain. Compression is not an optional extra for video streaming — it is what makes the service possible at all over an ordinary connection.

Nothing is discarded. Instead the data is described more efficiently, by recording patterns and repetitions rather than every individual item.

The standard example is run-length encoding (RLE), which replaces a run of repeated values with the value and a count.

The saving depends entirely on repetition. A picture with large areas of flat colour compresses dramatically; a detailed photograph where adjacent pixels differ may compress hardly at all — and RLE can even make such a file larger, since each single pixel now needs a count as well.

Another lossless technique replaces repeated words or phrases in a text file with a shorter code, storing an index that maps codes back to the original text.

This family of technique is called dictionary-based compression, and it underlies common general-purpose tools such as ZIP. Rather than working pixel by pixel like RLE, it scans for any repeated sequence of bytes — a common word, a repeated block of program code — and replaces later occurrences with a short reference back to the first one. This is why ordinary documents and program files, which contain far more repeated structure than a photograph does, often shrink substantially under lossless compression even though no pixel-style runs are involved.

RLE exploits repetition. A different lossless method, Huffman coding, exploits frequency instead: it gives the most common symbols the shortest binary codes and the rarest symbols the longest codes, instead of using a fixed number of bits for every symbol as ASCII does. A message dominated by one or two common characters can then be stored using far fewer bits per character on average.

The data removed is chosen to be what humans are least likely to notice:

These techniques are what give familiar file formats their purpose: JPEG applies lossy compression tuned for photographs, MP3 and AAC apply it to audio, and formats such as MPEG apply it to video. A camera or phone that offers a photo 'quality' setting is really letting the user choose how much lossy compression to apply — higher quality means less is thrown away, and a larger file results.

Lossy compression achieves much greater size reductions than lossless — often ten times smaller — which is why it is used for streaming music and video and for photographs on the web.

But the loss is permanent. Once the data is gone it cannot be recovered, and each further round of lossy compression degrades the file again. Repeatedly saving a photograph in a lossy format visibly damages it.

This is why lossy compression is never used for files where every byte matters: a compressed program would not run, a compressed spreadsheet would contain wrong numbers, and a compressed text document would lose words.

Ask one question: does the file still work if some data is missing?

That single test answers every 'which method should be used and why' question, and the justification should name both halves: why the loss is or is not tolerable, and what is gained.

Question. An image is $2048\times 1536$ pixels with a colour depth of 24 bits. (a) Calculate the file size in bits. (b) Convert to MiB. (c) State one way to reduce the file size without compression, and its effect.

Marking. 1 mark per point. Show every conversion step — method marks survive an arithmetic slip.

Question. A 4-minute recording uses a sample rate of $22050\text{Hz}$ and a sample resolution of 8 bits. (a) Calculate the file size in bits. (b) Convert to KiB. (c) The sample resolution is doubled to 16 bits — state the effect on file size and quality.

Marking. 1 mark per point. Converting minutes to seconds is the first marking point.

Question. (a) Define lossless compression. (b) Describe how run-length encoding compresses the pixel row $\text{AAAAABBBCCCCCC}$. (c) Explain why RLE would be a poor choice for a detailed photograph.

Marking. 1 mark per point. Part (c) rewards understanding that RLE depends on repetition, not just on being lossless.

Question. A company sends (i) a software installer and (ii) a music track to customers. State which compression method should be used for each and justify your choice.

Marking. 1 mark per point. Each justification must say why the loss is or is not tolerable and what is gained.