Every character a computer stores — letters, digits, punctuation, spaces — is held as a number, and that number is stored in binary. The character set is what decides which number means which character.

The agreement is essential. If one computer stored $65$ for 'A' and another used $65$ for something else, text would be unreadable when transferred. A shared standard is what makes text portable between systems.

This was not always the case. In the early decades of computing, manufacturers each used their own, incompatible codes — IBM mainframes, for example, commonly used a different scheme called EBCDIC. Exchanging a document between two different makes of computer could turn readable text into garbled symbols, because each side attached a different meaning to the same numbers. ASCII, standardised in the 1960s, was the industry's agreement to stop this from happening.

Two details are worth noticing. Codes for consecutive letters are consecutive numbers, so 'A' is 65, 'B' is 66, 'C' is 67 — which makes sorting alphabetically simple arithmetic.

And upper and lower case are different characters with different codes: 'A' is 65 but 'a' is 97. That is why a program must convert case explicitly before comparing text.

This numeric relationship is genuinely useful in programs, not just trivia: because 'a' is 97 and 'z' is 122, a program can test whether a character is a lower-case letter simply by checking that its code lies in that range, and can convert a lower-case letter to upper case by subtracting 32 from its code — the constant gap between 'a' (97) and 'A' (65), and between every other matching pair.

ASCII uses 7 bits, so it can represent $2^7=128$ different characters. That is enough for the English alphabet in both cases, the digits, punctuation and some control codes — and nothing else.

It cannot represent Greek, Arabic, Chinese, Hindi or any accented character. As computers became international this was untenable, so Unicode was developed using 16 bits or more, giving over a million codes — enough for most of the world's writing systems.

The cost is file size: Unicode uses at least twice as many bits per character as ASCII, so the same document stored in Unicode is at least twice as large. That is the trade-off the syllabus expects you to state.

Usefully, the first 128 Unicode codes are the same as ASCII, so ASCII text is already valid Unicode and older files still work.

A concrete example of the gap Unicode closes: the code point $\text{U+4E2D}$ represents the Chinese character 中 (meaning 'middle'), and $\text{U+1F600}$ represents 😀, a grinning-face emoji. Neither could ever exist inside ASCII's 128 codes — there simply is not room — which is exactly the problem Unicode was built to solve.

Sound is a continuously varying wave — an analogue quantity that takes any value at any instant. Binary can only store discrete numbers, so the wave must be converted.

This is done by sampling: measuring the amplitude of the wave at regular intervals and storing each measurement as a binary number.

The same trick already appears in cinema: a film is really a rapid sequence of still photographs — traditionally 24 per second — and the eye perceives continuous motion because the gaps between frames are too brief to notice. Digital audio does the same job in the time dimension: individual snapshots of amplitude, taken close enough together that the ear perceives an unbroken sound.

Between two samples the computer stores nothing — the original wave's behaviour in that gap is simply lost. Reconstruction joins the recorded points, producing a stepped approximation rather than the true smooth curve.

Taking samples more often and measuring each one more precisely both bring the approximation closer to the original — and both make the file larger. That is the whole trade-off in one sentence.

These are frequently confused, and questions often ask about one specifically:

An analogy: photographing a moving object. The rate is how many photographs per second; the resolution is how much detail is in each one. Increasing either improves the record, and both cost storage.

Both increase file size and both improve quality, so the answer to 'what happens if you increase X' is always the same pair — but the reason differs, and that is where the mark is.

An image is stored as a grid of pixels. Each pixel's colour is recorded as a binary number, and the file is the sequence of those numbers.

A real scene, like a real sound, is continuous — there is no smallest piece of it. Dividing it into a grid of pixels is the visual equivalent of sampling: the image is chopped into discrete units, and everything within one pixel is recorded as a single colour.

So detail smaller than one pixel is lost, which is exactly why enlarging a low-resolution image produces visible blocks rather than more detail. The detail was never stored.

This is why pixel density matters in practice: a printed photograph viewed from a normal reading distance can look sharp at around $300$ pixels per inch, while the same image viewed on a phone screen held much closer to the eye needs a higher density to look equally sharp. In both cases, detail finer than a single pixel's width simply cannot be shown, no matter how good the display is.

A colour depth of $n$ bits gives $2^n$ different colours. This is directly examinable in both directions:

So an image needing 100 distinct colours requires 7 bits, since $2^6=64$ is too few and $2^7=128$ is enough.

24-bit colour is the common standard for photographs: 8 bits each for red, green and blue, giving over 16 million combinations — more than the human eye can distinguish.

All three representations work identically: count the number of units, multiply by the bits per unit. Every file size calculation in the course is that single multiplication.

The two quality settings for sound and images map onto each other exactly:

Recognising this reduces four separate facts to one idea — and it explains why increasing any of the four improves quality and increases file size.

Question. A company stores documents in ASCII but is expanding internationally. (a) State how many characters ASCII can represent and why. (b) Explain why Unicode is needed. (c) State one disadvantage of changing to Unicode.

Marking. 1 mark per point. Part (a) needs the calculation $2^7$, not just the number 128.

Question. A sound is recorded at a sample rate of $44100\text{Hz}$ with a sample resolution of 16 bits, for 30 seconds. (a) Calculate the file size in bits. (b) Convert to megabytes. (c) State what happens to the file size and quality if the sample rate is doubled.

Marking. 1 mark per point. The formula gives bits — divide by 8 before converting to bytes, kilobytes or megabytes.

Question. An image is $800$ pixels wide and $600$ pixels high with a colour depth of 8 bits. (a) Calculate the file size in bits. (b) State how many colours can be used. (c) The colour depth is increased to 24 bits — state the effect on the number of colours and the file size.

Marking. 1 mark per point. Colour depth affects file size proportionally — tripling the bits per pixel triples the total.

Question. A photographer reduces both the resolution and the colour depth of an image. (a) Define each term. (b) Explain the effect of each reduction on the image. (c) State why the photographer might do this.

Marking. 1 mark per point. Each effect must be tied to its own setting — resolution to detail, colour depth to colours.