Bitlump Float Twiddler

IEEE 754 binary format

An IEEE 754 floating point number consists of three bit-fields: the sign bit, the exponent, and the mantissa.

Sign

The top bit is the sign bit.

Exponent

A floating point number has a base-2 exponent, indicating the power of two by which the mantissa must be multiplied.

In a XXX-bit XXX-precision float, the exponent field is bits.

An exponent field of all 0-bits indicates the value is zero or a subnormal number, and the true exponent is XXX. An exponent field of all 1-bits indicates an Infinity or NaN. In all other cases, the exponent field is stored biased by XXX, so the true exponent value is the raw value minus XXX.

Mantissa

The mantissa is the binary fraction which must be multiplied by 2^exponent to produce the final value.

In a XXX-bit XXX-precision float, the mantissa field stores XXX bits. These are the bits after the mantissa's binary point; the single leading bit, before the binary point, is implied. The implied bit's value is usually 1, but it is 0 for subnormal numbers (see above) and zero. Therefore, the true value of the mantissa is in the range 1 ≤ mantissa < 2, except for subnormal numbers and zero, where it is in the range 0 ≤ mantissa < 1.

Value

The overall value is given by:

signvalue × 2^exponent × mantissa

where signvalue is 1 if the number is positive or -1 if negative.

Limits and constants

The following limits and attributes apply to IEEE 754 XXX-precision floating point numbers.