• Units of data are built from the bit upward — bit → nibble → byte → kibibyte → mebibyte → gibibyte, and so on — each one 1024× the size of the last (once you're past a byte).
• Kilobyte ≠ Kibibyte. Kilobyte (KB) uses powers of 10 (1000), Kibibyte (KiB) uses powers of 2 (1024). Exam answers almost always want the 1024 (binary) version.
• Converting units is just repeated multiplying or dividing by 1024 (or by 8 for bits↔bytes) — the direction depends on whether you're going up or down in size.
• Bitmap image file size = resolution (number of pixels) × colour depth (bits per pixel).
• Sound file size = sample rate × duration × sample resolution.
• Compression shrinks files to save storage space, reduce bandwidth use, and cut transmission time.
• Lossy compression permanently throws away some data — smaller files, but quality is reduced forever. Used for photos, video, music.
• Lossless compression is fully reversible — no data is lost, just re-encoded more efficiently. Used for documents, code, anything where accuracy matters.
• Run Length Encoding (RLE) is a lossless technique that replaces repeated ("runs" of) identical values with a shorter code showing the value and how many times it repeats.

What actually is a "unit of data"?

Deep down, a computer only ever stores binary digits — 1s and 0s. A single one of these is called a bit (short for ). On its own, one bit can't say much — it can only be "on" or "off". So we group bits together into bigger and bigger chunks to represent more meaningful amounts of information, the same way we don't measure a person's height in millimetres — we group millimetres into centimetres, then metres.

Why does a byte matter so much? A single byte (8 bits) can represent 2⁸ = 256 different values — which happens to be enough to represent every letter, number, and symbol on a standard keyboard (that's exactly why the ASCII character set fits in one byte). This makes the byte the "natural" building block computers are organised around.

Kilobyte vs Kibibyte — the exam trap

You will see two very similar-looking units and it's extremely easy to mix them up:

• 1 kilobyte (KB) = 1000 bytes — this uses prefixes (powers of 10), the same system marketers use when they sell you a "500 GB" hard drive.
• 1 kibibyte (KiB) = 1024 bytes — this uses prefixes (powers of 2), which is how the computer itself actually addresses memory internally.

For IGCSE, unless a question specifically says "decimal" or gives you the KB/1000 system, always work in 1024s (KiB, MiB, GiB…) — this is the version the syllabus and mark schemes expect.

Converting between units

Quick way to remember the direction: ask yourself "am I ending up with a bigger number or a smaller number?" If your file is 2 tebibytes and you want it in gibibytes, you know gibibytes are much smaller units, so there must be of them — multiply. If you're going from kibibytes up to mebibytes, mebibytes are a bigger unit, so there will be of them — divide.

Bitmap image file size

A bitmap image is just a huge grid of coloured squares called pixels. Each pixel needs some number of bits to store its colour — the more bits you give it, the more possible colours it can be (this is called the colour depth). To work out the total file size, you just need to know how many pixels there are, and how many bits each one costs.

So really there are two equivalent formulas — pick whichever the question gives you numbers for:

Sound file size

Digital audio is recorded by "sampling" the sound wave thousands of times per second — imagine taking a tiny snapshot of the wave's height at regular intervals and writing down the number each time. Three things control the file size: how you sample (sample rate), how you record for (duration), and how much you store per sample (sample resolution).

Why do we compress files at all?

Compression means reducing the size of a file so it takes up less space on secondary storage (like a hard drive or SSD). Think about how many photos, songs, and videos you have on your phone — without compression, you'd run out of storage almost instantly, and sending even one photo over the internet would take forever.

Compression gives us three big wins:

• Less storage space required — you can fit more files on the same device.
• Less bandwidth required — smaller files use less of your internet connection's capacity.
• Shorter transmission time — smaller files upload/download/transfer faster.

There are two completely different strategies for compressing a file, and the exam expects you to know exactly how they differ: lossy and lossless.

What is lossy compression?

Lossy compression makes a file smaller by permanently throwing some data away. Once it's gone, it's gone — you can never get the file back to its exact original state. This sounds bad, but it's actually a smart trade-off: for things like photos, video and music, our eyes and ears often can't detect the difference anyway, so we can lose a lot of data before anyone notices.

A classic example: in a photograph, lossy compression looks for similar colours sitting near each other and merges them into a single colour, reducing the total number of unique colours stored — the human eye usually can't spot the difference, but the file becomes dramatically smaller.

What is lossless compression?

Lossless compression shrinks a file by encoding the data more cleverly — finding smarter, shorter ways to represent exactly the same information — rather than deleting any of it. When you "decompress" (open) the file, the original data is rebuilt perfectly, bit for bit. Nothing is missing.

The trade-off is that lossless compression usually can't shrink a file as much as lossy compression can, because it's not allowed to throw anything away. It's more suitable for data where accuracy is essential — documents, program code, spreadsheets — where losing even one character could break everything.

Run Length Encoding (RLE)

RLE is one specific lossless algorithm you need to know in detail. It works by scanning data for runs — sequences where the exact same value repeats over and over — and replacing each run with just two pieces of information: the repeated value is, and it repeats.

Text example:

Image example: RLE is especially powerful for bitmap images that contain large blocks of a single flat colour — like a cartoon drawing, a logo, or a scanned document with big white backgrounds. A row of pixels with 5 red pixels followed by 3 blue pixels could be represented as simply 5R3B instead of storing all 8 individual pixel values.