6.6.3 Zero, Infinity, Not a Number (NaN) and Subnormal Values

The IEEE 754-2008/2019 standards reserve data encoding to represent special values, as shown in Figure 6-19.

Zero is conveyed when both exponent and mantissa are all 0’s. Zero is a signed value (for some operations) as determined by the Sign bit. Infinity is conveyed by an exponent value of all 1’s with an all 0’s mantissa. Infinity is a signed value as determined by the Sign bit.

A Signaling NaN is conveyed by an exponent value of all 1’s with the MSb of the mantissa set to 0 (remaining mantissa bits may be set to any value). The Quiet Nan (qNaN, see Not a Number (NaN)) is conveyed by an exponent value of all 1’s with the MSb of the mantissa set to 1 (remaining mantissa bits may be set to any value). NaN values are not signed, so the Sign bit may be any state.

A Subnormal value (see Subnormal Number) is conveyed by an exponent of all 0’s and any non-zero mantissa value. Subnormals are signed values as determined by the Sign bit.