Significand

A number is, in general, represented approximately to a fixed number of significant digits (the significand ) and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen.

Explicitly, ignoring significand, taking the reciprocal is just taking the additive inverse of the (unbiased) exponent, since the exponent of the reciprocal is the negative of the original exponent.

Here, s denotes the significand and e denotes the exponent.

In practice, the most significant bit of the significand field determined whether a NaN is signaling or quiet.

In the case of a tie, the value that would make the significand end in an even digit is chosen.

In the IEEE binary interchange formats the leading 1 bit of a normalized significand is not actually stored in the computer datum.

Let's see what this format looks like by showing how such a number would be stored in 8 bytes of memory: where "S" denotes the sign bit, "x" denotes an exponent bit, and "m" denotes a significand bit.

Rounding modes Rounding is used when the exact result of a floating-point operation (or a conversion to floating-point format) would need more digits than there are digits in the significand.

The decimal separator in the significand is shifted x places to the left (or right) and x is added to (or subtracted from) the exponent, as shown below.

The significand is a binary fraction that doesn't necessarily perfectly match a decimal fraction.

The way in which the significand (including its sign) and exponent are stored in a computer is implementation-dependent.

This holds even for the last step from a given exponent, where the significand overflows into the exponent: with the implicit 1, the number after 1.11.