     suivant: Examples of representations of monter: Floating point representation. précédent: Digits   Table des matières   Index

## Representation by hardware floats

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

d = 2 *(1 + m),    0 < m < 1, -210 < < 210

If > 1 - 210, then m 1/2, and d is a normalized floating point number, otherwise d is denormalized ( = 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:
• 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 +210 - 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/253 for normalized floats and m = M/253 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
• = 210 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