Datasheet

Floating-point Support

Numbers stored in the above form are called normalized numbers.

The maximum and minimum exponent values, 0 and 255, are special cases. Exponent

255 is used to represent infinity, and store Not a Number (NaN) values. Infinity can

occur as a result of dividing by zero, or as a result of computing a value that is too large

to store in this format. NaN values are used for special purposes. Infinity is stored by

setting Exp to 255 and Frac to all zeros. If Exp is 255 and Frac is nonzero, the bit pattern

represents a NaN.

Exponent 0 is used to represent very small numbers in a special way. If Exp is zero, then

the Frac field has no implicit 1 on the front. This means that the format can store 0.0, by

setting both Exp and Frac to all 0 bits. It also means that numbers that are too small to

store using Exp >= 1 are stored with less precision than the ordinary 23 bits. These are

called denormals.

Double precision

double

value is 64 bits wide. Figure 5-4 shows its structure.

Figure 5-4 IEEE 754 double-precision floating-point format

As before, S is the sign, Exp the exponent, and Frac the fraction. Most of the discussion

float

values remains true, except that:

• The Exp field is biased by

0x3FF

(1023) instead of

0x7F

, so numbers between 1.0

and 2.0 have an Exp field of

0x3FF

• The Exp value used to represent infinity and NaNs is

0x7FF

(2047) instead of

0xFF

63 52 5162 0

Exp Frac