Know that data is stored in bits and bytes, the units from bit to terabyte, and calculate file sizes and storage requirements.

What this dot point is asking

AQA wants you to know that data is stored in bits and bytes, recall the units from bit up to terabyte, and calculate file sizes and storage requirements, showing each conversion step.

Bits and bytes

The larger units

You may have read that a kilobyte is "really" 1024 bytes. That is the older binary (kibibyte) convention. For the 8525 specification AQA uses powers of 1000 unless a question explicitly tells you otherwise, so use 1000 every step. Storage manufacturers also quote capacities in powers of 1000, which is why a "500 GB" drive shows as slightly less in some operating systems that count in 1024s.

Calculating file sizes

The single most useful habit is to write the calculation as a chain: bits, then bytes (divide by 8), then KB or MB (divide by 1000 each step). Doing it in stages makes part-marks easy to earn even if you slip on the final unit.

Why a byte is 256 values

A single byte of 8 bits can represent $2^8 = 256$ different values, from 0 to 255. This is the reason a byte became the standard unit: 256 values is enough to give every character in the original ASCII set its own code with room to spare. The pattern $2^n$ recurs throughout the topic, because $n$ bits always give $2^n$ combinations: 1 bit gives 2 values, 4 bits (a nibble) give 16, and 8 bits give 256. Recognising this lets you answer questions about how many colours a colour depth allows, how many characters a code can represent, or how many amplitude levels a bit depth gives, all from the same rule.

Working through a multi-step file-size question

Exam file-size questions often combine several steps, so always lay them out as a chain. First find the total bits using the right formula for the medium (image: width times height times colour depth; sound: sample rate times bit depth times duration; text: characters times bits per character). Then divide by 8 to get bytes. Then divide by 1000 for each step up to KB, MB or whatever the question asks. Writing each stage separately means a slip in one step still earns the method marks for the others, and it makes it obvious whether you have answered in the unit the question requested.

Try this

Q1. State how many bits are in a byte. [1 mark]

• Cue. 8 bits.

Q2. Calculate the file size in bytes of a 50 by 40 pixel image with a colour depth of 4 bits per pixel. [2 marks]

• Cue. $50 \times 40 \times 4 = 8000$ bits, then $8000 \div 8 = 1000$ bytes.