A NUMBER IN 32 BITS

sign, exponent and significand: what actually sits in a float and what does not

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: code · reference · study

The strip at the top is the thirty-two bits of one constant, cut into three fields in the proportion 1 : 8 : 23. The middle table says what the exponent field means in each of five cases; the lower one, how closely the numbers sit at different places along the line.

EVERY FLOAT IS EXACT — JUST NOT THE ONE YOU ASKED FOR

Floats are said to be “approximate”. In fact every float is an exact number, and it can be written out in full in decimal digits: its denominator is always a power of two, so the fraction ends.

What is approximate is not the number but how it answers the one you asked for. Write 0.1 and what goes into 32 bits is 0.100000001490116119384765625, exactly and with nothing left over. That is why ten of them do not add up to one: what is being added is not a tenth but this.

On the sheet

The strip at the top is the thirty-two bits of one constant, cut into three fields in the proportion 1 : 8 : 23. The middle table says what the exponent field means in each of five cases; the lower one, how closely the numbers sit at different places along the line.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 8 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

A NUMBER IN 32 BITS

EVERY FLOAT IS EXACT — JUST NOT THE ONE YOU ASKED FOR

On the sheet

Printing

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