Text, images and sound as bits

Character sets

A computer can only store numbers. So every character is given a number code.

A character is any letter, digit, punctuation mark, space or symbol.

A character set is the full list of characters a computer can use, with the binary code for each one.

When you press a key, the keyboard sends the code. The screen looks up the code and draws the character.

ASCII

ASCII (American Standard Code for Information Interchange) uses 7 bits per character. That gives 2⁷ = 128 characters.

It covers English letters, digits, punctuation and some control codes like "new line".

Extended ASCII uses 8 bits, giving 256 characters. The extra ones add some accented letters and symbols.

Codes run in order. A is 65, so B is 66 and C is 67. Lowercase a is 97, which is 32 more than A.

Unicode

Unicode is a much bigger character set. It can use up to 32 bits (4 bytes) per character.

It has room for over a million characters. It covers almost every written language, maths symbols and emojis.

The first 128 Unicode codes are the same as ASCII, so ASCII text still works.

The cost: Unicode uses more bits per character, so text files can be bigger.

Sound: sampling

Real sound is a wave. It changes smoothly, so it is called analogue.

A computer cannot store a smooth wave. It measures the height (amplitude) of the wave at fixed time gaps.

Each measurement is a sample. Each sample is stored as a binary number.

This is called sampling. The stored samples are a close copy of the wave, not a perfect one.

There is a diagram for this step in the IGCSE library.

Sample rate and sample resolution

Sample rate is the number of samples taken each second. It is measured in hertz (Hz). 44,100 Hz means 44,100 samples every second.

Sample resolution is the number of bits used to store each sample. 16 bits gives 2¹⁶ = 65,536 possible heights.

A higher sample rate catches quicker changes in the wave. A higher sample resolution measures each height more precisely.

Both make the recording more accurate and closer to the real sound. Both also make the file bigger.

Images: pixels and resolution

A bitmap image is a grid of tiny squares called pixels (picture elements).

Each pixel is one colour. Each colour is stored as a binary number.

Image resolution is the number of pixels in the image. It is written as width × height, for example 1920 × 1080.

More pixels show more detail, so the image is sharper. But more pixels need more bits, so the file is bigger.

Colour depth

Colour depth is the number of bits used to store the colour of each pixel.

With n bits per pixel you can show 2ⁿ different colours.

Greater colour depth gives more colours, so shades look smoother and more real. It also makes the file bigger.

24-bit colour uses 8 bits for red, 8 for green and 8 for blue. That is two hex digits each, as in #FF8800.

Units of data

A bit is one 0 or 1. A nibble is 4 bits. A byte is 8 bits.

After the byte, each unit is 1024 times bigger than the one before.

1024 is used because it is a power of 2: 2¹⁰ = 1024. Computers count in powers of 2.

Try the toy: type 1 and choose GiB. Read the MiB and KiB rows in the table. How many times did you multiply by 1024 to reach KiB?

There is something to try for this step in the IGCSE library.

Converting between units

Going to a smaller unit: multiply (× 1024, or × 8 from bytes to bits).

Going to a bigger unit: divide (÷ 1024, or ÷ 8 from bits to bytes).

Move one unit at a time and write each step. It is slower but it avoids mistakes.

Calculating image file size

Every pixel needs the same number of bits: the colour depth.

So file size in bits = number of pixels × colour depth. Number of pixels = width × height.

Then divide by 8 for bytes, by 1024 for KiB, and by 1024 again for MiB.

Real files are a little bigger, because they also store extra data such as the width and height.

Calculating sound file size

Each second you take (sample rate) samples. Each sample uses (sample resolution) bits.

So file size in bits = sample rate × sample resolution × length in seconds.

Then divide by 8 for bytes and by 1024 for KiB or MiB, as for images.

This is for one channel (mono). Change minutes into seconds first.

Why we compress files

Compression makes a file smaller, so it uses fewer bits.

Smaller files use less storage space on a device or server.

Smaller files need less bandwidth. Bandwidth is how much data a connection can carry each second.

So smaller files are sent faster: quicker downloads, quicker uploads, and less buffering when streaming.

Many services set a size limit. An email attachment limit of 25 MB is a real example.

Lossy compression

Lossy compression removes data permanently. You can never get the original back.

It removes detail people are unlikely to notice, such as sounds humans cannot hear or tiny colour differences.

Ways to do it: lower the image resolution or colour depth, or lower the sample rate or sample resolution.

Examples: JPEG for photos, MP3 for music, and most video streaming.

It gives a much smaller file than lossless, but quality is lower.

Lossless compression

Lossless compression makes the file smaller without losing any data.

When the file is decompressed, it is exactly the same as the original, bit for bit.

It finds patterns and repeats in the data and stores them in a shorter way.

Use it when every bit matters: text, program files, spreadsheets, medical scans.

The file is not made as small as with lossy compression.

Run-length encoding (RLE)

Run-length encoding (RLE) is a lossless method. A run is a group of the same value in a row.

RLE stores each run as two values: how many, then which value.

It works well when data has long runs, such as simple images with big areas of one colour.

Try the toy: press All one colour, then press Stripes so every pixel is different from the next. Compare the sizes before and after RLE.

There is something to try for this step in the IGCSE library.

RLE: working out the saving

To judge compression, compare the size before and after.

RLE only helps when runs are long. If values change all the time, RLE can make the file bigger.

That is why RLE suits simple graphics and icons, but not photographs.