I am wondering if the max float represented in IEEE 754 is:
(1.11111111111111111111111)_b*2^[(11111111)_b-127]
Here _b
means binary representation. But that value is 3.403201383*10^38
, which is different from 3.402823669*10^38
, which is (1.0)_b*2^[(11111111)_b-127]
and given by for example c++
<limits>
. Isn't
(1.11111111111111111111111)_b*2^[(11111111)_b-127]
representable and larger in the framework?
Does anybody know why?
Thank you.
So there are 2^32 - 2^25 = 4261412864 distinct normal numbers in the IEEE 754 binary32 format.
The IEEE-754 standard describes floating-point formats, a way to represent real numbers in hardware. There are at least five internal formats for floating-point numbers that are representable in hardware targeted by the MSVC compiler. The compiler only uses two of them.
Consequently, the smallest non-zero positive number that can be represented is 1×10−101, and the largest is 9999999×1090 (9.999999×1096), so the full range of numbers is −9.999999×1096 through 9.999999×1096.
The exponent 11111111b is reserved for infinities and NaNs, so your number cannot be represented.
The greatest value that can be represented in single precision, approximately 3.4028235×1038, is actually 1.11111111111111111111111b×211111110b-127.
See also http://en.wikipedia.org/wiki/Single-precision_floating-point_format
Being the "m" the mantisa and the "e" the exponent, the answer is:
In your case, if the number of bits on IEEE 754 are:
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