Max float introduced in IEEE 754

Question

I am wondering if the max float is represented in IEEE 754:

(1.11111111111111111111111)_b*2^[(11111111)_b-127]

Here _bmeans binary representation. But this value 3.403201383*10^38, which is different from 3.402823669*10^38that (1.0)_b*2^[(11111111)_b-127]and set, for example c++ <limits>. not (1.11111111111111111111111)_b*2^[(11111111)_b-127]conceivable and more within?

Does anyone know why?

Thank.

Answer 1

Indicator 11111111 _b reserved for infinity and NaN, so your number cannot be represented.

The largest value that can be represented in single precision, approximately 3.4028235 × 10 ³⁸ is actually 1.1111111111111111111111111 _b × 2 ^{11111110 _{b > -127}}.

. http://en.wikipedia.org/wiki/Single-precision_floating-point_format

Answer 2

" " " " , :

, IEEE 754 :

• 16 1 , 6 11 . 4 293 918 720 .
• 32 1 , 8 23 . - 3.402823466E38.
• 64 1 , 11 52 . - 2 ^ 1024 - 2 ^ 971