为什么两个连续的转换会更改一个整数？

Question

I wrote the below program :

#include <iostream>

int main()
{
   int i =123456789;
   float f=i;
   int j=f;
   std::cout<<"j-i ="<<j-i;
}

As far as we know, float numbers has at least 4 byte length in the memory. and 123456789 in decimal is equal with 0x75BCD15 in hexadecimal and this is less than 4 byte. So I why when I run the above program, the output is not 0 ?

ap1019@sharifvm:~$ ./a.out
j-i = 3

Answer 1

Because float only has 23 bits of precision (*). The other 9 bits are needed for the sign and the exponent. This means that after 16,777,216 you get holes in the "whole numbers" float range.

(*) Actually 24 bits, but only 23 bits need to be stored; the first bit is implied by the exponent.