Bits, bytes and binary. — Making Software

Binary is a compact agreement: two reliable physical states become digits that can represent numbers, text, instructions and media. The apparent simplicity comes from a set of carefully chosen representations, transformations and physical assumptions working together.

Place value

Each binary position is worth twice the position to its right.

This is one part of a longer chain: physical state becomes bit becomes byte becomes meaning. The useful abstraction hides the physical work, but the underlying constraints still shape the software built above it.

Signed numbers

Two’s complement lets the same arithmetic hardware handle positive and negative values.

The implementation is full of compromises. Precision, speed, storage and energy rarely improve together, so practical systems choose the errors people are least likely to notice.

Encoding

Meaning comes from convention: the same byte can be a number, character or colour channel.

Once this layer is visible, familiar design conventions stop looking arbitrary. They are accumulated responses to the capabilities and limits of the machinery below.