#### 15.2.1 Binary Floating-point Representation

Although floating-point representations vary from machine to machine,
the most commonly encountered representation is that defined by the
IEEE 754 Standard. An IEEE-754 format value has three components:

- A sign bit telling whether the number is positive or negative.
- An exponent,
`e`, giving its order of magnitude.
- A significand,
`s`,
specifying the actual digits of the number.

The value of the
number is then
`s * 2^e`.
The first bit of a non-zero binary significand
is always one, so the significand in an IEEE-754 format only includes the
fractional part, leaving the leading one implicit.
The significand is stored in normalized format,
which means that the first bit is always a one.

Three of the standard IEEE-754 types are 32-bit single precision,
64-bit double precision and 128-bit quadruple precision.
The standard also specifies extended precision formats
to allow greater precisions and larger exponent ranges.