Floating point: definition · Chip Field Guide

Beginner

A way of storing numbers like scientific notation: a few digits plus a note saying where the decimal point goes, so the same few digits can describe tiny or huge numbers.

Novice

A number format that stores a sign, an exponent and a mantissa. The value is $\pm(1.\text{mantissa}) \times 2^{\text{exponent} - \text{bias}}$ . Because the exponent moves the binary point, the format covers a huge range with a fixed number of significant bits.

Expert

Binary floating point per IEEE 754 and its descendants: significand precision $p$ (mantissa bits + 1 hidden bit), exponent width setting the range in binades, round-to-nearest-even, subnormals for gradual underflow. Relative rounding error is bounded by $2^{-p}$ regardless of magnitude.