suivant: Examples of representations of
monter: Floating point representation.
précédent: Digits
Table des matières
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A real is represented by a floating number d, that is
d = 2
^{}*(1 +
m), 0 <
m < 1, 2
^{10} <
< 2
^{10}
If
> 1  2^{10}, then
m 1/2, and d is
a normalized floating point number, otherwise
d is denormalized (
= 1  2^{10}). The special exponent 2^{10}
is used to represent plus or minus infinity and NaN (Not a Number).
A hardware float is made of 64 bits:
 the first bit is for the sign of d (0 for '+' and 1 for '')
 the 11 following bits represents the exponent, more precisely
if denotes the integer from the 11 bits,
the exponent is
+2^{10}  1,
 the 52 last bits codes the mantissa m, more precisely if
M denotes the integer from the 52 bits, then
m = 1/2 + M/2^{53} for normalized floats and
m = M/2^{53} for
denormalized floats.
Examples of representations of the exponent:
 = 0 is coded by 011 1111 1111
 = 1 is coded by 100 0000 0000
 = 4 is coded by 100 0000 0011
 = 5 is coded by 100 0000 0100
 =  1 is coded by 011 1111 1110
 =  4 is coded by 011 1111 1011
 =  5 is coded by 011 1111 1010

= 2^{10} is coded by 111 1111 1111

= 2^{10}  1 is coded by 000 0000 000
Remark:
2^{52} = 0.2220446049250313e  15
suivant: Examples of representations of
monter: Floating point representation.
précédent: Digits
Table des matières
Index
giac documentation written by Renée De Graeve and Bernard Parisse