Images and text as numbers.

Step 1 of 6

Resolution

A digital picture is a grid of pixels. Its resolution is how many pixels it has across and down; here the picture keeps a 4 : 3 shape, so its height is three quarters of its width. The more pixels, the smoother the edges, and the bigger the file.

The picture is now 32 pixels across, and the board shows the number of pixels and the size. Predict, and then Pixels across will double.

Step 2 of 6

The file size

The size of an uncompressed picture is a simple sum:

$B = \frac{P \times 3 \times s}{8}$$B =$$\frac{P \times 3 \times s}{8}$⁠

where $B$⁠ is the size in bytes, $P$⁠ the number of pixels and $s$⁠ the bits per channel: three channels per pixel, and dividing by $8$⁠ turns bits into bytes. Real files, like JPEG and PNG, compress these numbers, but the screen always shows the full picture.

Step 3 of 6

Resolution against colour

The same file size can be reached two ways: more pixels with fewer bits each, or fewer pixels in rich colour. Small icons and the pictures in old games gave up colours to save space.

Step 4 of 6

Letters as numbers

Text is numbers too. An encoding is a table that gives every character a number, and the computer stores only the numbers. The old encoding, ASCII, from the 1960s, numbers every Latin letter, digit and punctuation mark: A is $65$⁠, a is $97$⁠, the digit 0 is $48$⁠ and the space $32$⁠. It has $128$⁠ characters, seven bits, so each character fits in one byte.

Step 5 of 6

A word

A word is just a run of characters, and each one is stored separately, in order. Spaces and punctuation marks are characters too, and take room like a letter.

Step 6 of 6

Every language

ASCII has no room for Hebrew, Arabic, Chinese or emoji. Unicode gives a number to every character in every script in the world, more than a hundred and fifty thousand of them. The UTF-8 encoding stores them in one to four bytes: ASCII characters stay at one byte, so old text works as before, and other characters take more.