Use units of storage from bit to terabyte, and explain lossless and lossy compression and why files are compressed

What this dot point is asking

SEAB wants you to use the units that measure amounts of data, from the bit up to the terabyte, to work out simple file sizes, and to explain compression: what lossless and lossy compression are, how they differ, and why files are compressed at all. The central idea is that all storage is measured in multiples of the byte, and compression trades some combination of detail or processing for a smaller file.

The answer

Units of storage

The smallest unit is the bit (one binary digit). Eight bits make a byte. Above the byte, each unit is about $1000$ times the one below it (using the common decimal convention):

Strictly, computers count in powers of two, so $1\ \text{KB} = 1024$ bytes, but at O-Level the round figure of $1000$ is accepted unless a question says otherwise.

Calculating a simple file size

To estimate a file size, work out the total bits and convert to bytes. For an image, multiply the number of pixels by the colour depth:

total bits = number of items x bits per item
total bytes = total bits / 8

Why we compress files

Compression makes a file smaller. This saves storage space, speeds up transfer over a network (less data to send), and uses less bandwidth, which matters for streaming, email attachments and web pages.

Lossless compression

Lossless compression reduces the size without losing any data, so the original file can be restored exactly. It works by storing information more efficiently, for example recording a repeated pattern once with a count. It is used where every bit matters: text documents, spreadsheets, program code and some image formats.

Lossy compression

Lossy compression achieves much smaller files by permanently removing detail that a person is unlikely to notice, such as subtle colours in a photo or sounds the ear cannot easily hear. The original cannot be fully restored. It is used for photos, music and video, where a small loss of quality is an acceptable price for a much smaller file.

Examples in context

Example 1. Streaming a video. A streaming service uses lossy compression so a film fits the viewer's internet speed. The picture loses a little fine detail, but it can be sent smoothly in real time, which would be impossible with the full uncompressed data.

Example 2. Zipping a folder of documents. A student zips a folder of reports and code before emailing it. The zip uses lossless compression, so when the recipient unzips it, every document and line of code is restored exactly, with nothing lost.

Try this

Q1. State how many bytes are in one megabyte, using the decimal convention. [2 marks]

• Cue. About $1000$ kilobytes, so about $1\,000\,000$ bytes.

Q2. Give two reasons a website might compress its images. [2 marks]

• Cue. Smaller files load faster for users and use less bandwidth and storage.

Q3. A file must be restored to its exact original after transfer. State which type of compression must be used and why. [2 marks]

• Cue. Lossless, because it loses no data and so the original can be rebuilt exactly.