H.1 Basic Formats

Numbers in the single and double formats are composed of the following three fields:

1.

1-bit sign s

2.

Biased exponent e = E + bias

3.

Fraction $f= \bullet b_{1} b_{2} \cdots b_{p-1}$

The range of the unbiased exponent E shall include every integer between two values E_min and E_max, inclusive, and also two other reserved values E_min-1 to encode ±0 and denormalized numbers, and E_max+1 to encode $\pm \infty$ and NaNs. The foregoing parameters are given in Table H.1. Each nonzero numerical value has just one encoding. The fields are interpreted as follows:

 

$$\geq 32 \geq 64$$ p 24 53

$$\geq +1023 \geq +16383$$ E_max +127 +1023

$$\leq -1022 \leq -16382$$ E_min -126 -1022

+127 unspecified +1023 unspecified

$$\geq 11 \geq 15$$ Exponent width in bits 8 11

$$\geq 43 \geq 79$$ Format width in bits 32 64