Numeric data types comparison in C#

Question

Could you please explain the results of the following code:

    float f = 1.56898138E+09f;
    double d = 1.56898138E+09;
    int i = 1568981320;

    bool a = f > i; //false 
    bool b = d > i; //true
    bool c = (int)f > i; //true

Why is a == false?

Answer 1

Well, int uses all 32 bits to store the integer value

 1568981320 == 1011101100001001100000101001000 (binary)

when float uses 23 bits only with first is always 1 (https://en.wikipedia.org/wiki/Single-precision_floating-point_format), so the initial 1011101100001001100000101001000 should be rounded:

 1011101100001001100000101001000
                         ^ 
 ^                       from this on we should throw the "1001000" bits away
 |   
 this 1 can be skipped since float assumes that the 1st bit is always 1 

So when rounding we should throw 1001000 away and add 1:

 1011101100001001100000101001000 - original value (1568981320)

 1011101100001001100000110000000 -  rounded value (1568981376)
  ^                     ^
  will be stored in float   

and this is 1568981376 value which is bigger than original 1568981320