c++ - IA64 doesn't correspond to IEEE standard for float numbers?

Question

I tried this code to represent float number storing system:

float *f = new float();
int *i = new int();
i = reinterpret_cast<int *>(f);
std::bitset<32> *bs;

std::cin>>*f;
bs = new std::bitset<32>(*i);
std::cout<<*bs<<" == "<<*f<<std::endl;

But when it run with 23.5 the result is 01000001-10111100-00000000-00000000. The power is 10000001=63.
Shouldn't it be 64 due to IEEE standard?
And the mantis should be 00010111-10000000-00000000. Is that true?

Note: I compiled this code with GCC and VS both. The result was same.

Answer 1

01000001-10111100-00000000-00000000

0 10000011 01111000000000000000000

sign: 0
exponent: 10000011_binary = 131_decimal
mantissa: 01111000000000000000000_binary
mantissa is defined by 1.<mantissa>
so -> 1.01111_binary

exponent is defined this way: exp-127
-> 131-127 = 4
-> 1.01111_binary * 2^4
-> comma shift to the right by 4 
--> 10111.1_binary = 23.5_decimal

一般来说：

(-1)^sign * 1.<mantissa> * 2^(exponent-127)