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4.1.2  Representation by hardware floats

A real is represented by a floating number d, that is

d=2(1+m),     0<m<1, −210 < α < 210 

If α>1−210, then m ≥ 1/2, and d is a normalized floating point number, otherwise d is denormalized (α=1−210). The special exponent 210 is used to represent plus or minus infinity and NaN (Not a Number). A hardware float is made of 64 bits:

Examples of representations of the exponent:

Remark: 2−52=0.2220446049250313e−15


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