IEEE Standard 754-2008

IEEE Standard 754-2008, and the 754-2018 revision

Standard Float64 bitfields

the representation

2.1.26 floating-point representation: An unencoded member of a floating-point format, representing a

finite number, a signed infinity, a quiet NaN, or a signaling NaN. A representation of a finite number has three components: a sign, an exponent, and a significand; its numerical value is the signed product of its significand and its radix raised to the power of its exponent.

Standard Floating Point Specifications

This view of the significand as an integer c, with its corresponding exponent q, describes exactly the same set of zero and non-zero floating-point numbers as the view in scientific form. [§3.3]

the sign

the significand

2.1.49 significand: A component of a finite floating-point number containing its significant digits. The

significand can be thought of as an integer, a fraction, or some other fixed-point form, by choosing an appropriate exponent offset. A decimal or subnormal binary significand can also contain leading zeros.

the exponent

2.1.19 exponent: The component of a finite floating-point representation that signifies the integer power to

which the radix is raised in determining the value of that floating-point representation. The exponent e is used when the significand is regarded as an integer digit and fraction field, and the exponent q is used when the significand is regarded as an integer; e = q + p − 1 where p is the precision of the format in digits.