Representation of Floating Point numbers

Code:

#include <iostream>
using namespace std;

void print_binary_representation(unsigned int x)
{
    size_t siz = 8*sizeof(x);    // sizeof returns size in bytes.
    for (size_t i = siz; i>0; i--)
    {
        int val = (((x >> (i-1)) << (siz-1)) >> (siz-1));
        cout << val;
        if ( i == 32 || i == 24)
            cout << ",";
    }
    cout << endl;
}


int main()
{
    float x = 2.0;
   
    cout << "Size of float: " << sizeof(float) << endl;
    cout << "Size of unsigned int: " << sizeof(unsigned int) << endl;

    do
    {
        void *vx = &x;
        unsigned int xui = *(unsigned int*)vx;
        unsigned int xui_direct = (unsigned int)x;
        cout << "Representation of " << x << " as unsigned int: " << xui << ", binary: ";
        print_binary_representation(xui);
        cout << "Enter number: ";
        cin >> x;
    }while( x != 1234);
   
    return 0;
}

Output:

Size of float: 4
Size of unsigned int: 4
Representation of 2 as unsigned int: 1073741824, binary: 0,10000000,00000000000000000000000
Enter number: -4
Representation of -4 as unsigned int: 3229614080, binary: 1,10000001,00000000000000000000000
Enter number: 8
Representation of 8 as unsigned int: 1090519040, binary: 0,10000010,00000000000000000000000
Enter number: -8
Representation of -8 as unsigned int: 3238002688, binary: 1,10000010,00000000000000000000000
Enter number: 123456
Representation of 123456 as unsigned int: 1206984704, binary: 0,10001111,11100010010000000000000
Enter number: -123456
Representation of -123456 as unsigned int: 3354468352, binary: 1,10001111,11100010010000000000000
Enter number: 1234

Using Visual Studio 2012 64-bit Compiler.

Number	Sign	Exponent	Fraction	Exp-val	expected expansion of fraction
4	0	10000001	00000000000000000000000	2	1
-4	1	10000001	00000000000000000000000	2	1
8	0	10000010	00000000000000000000000	3	1
-8	1	10000010	00000000000000000000000	3	1
123456	0	10001111	11100010010000000000000	16	1.883789063
-123456	1	10001111	11100010010000000000000	16	1.883789063
2.76	0	10000000	01100001010001111010111	1	1.38

In the above table, the Sign-Exponent-Fraction columns form the binary representation of "Number" in a float type.
Note that in "expected expansion of fraction" column, all numbers start are of the form 1.*. So while storing the fraction portion this 1 is omitted and Fraction expands only to the part after decimal point. For e.g. 01100001010001111010111 evaluates to 0.38
example of decimal to binary fraction conversion:

0.38	0.76	0
0.76	1.52	1
0.52	1.04	1
0.04	0.08	0
0.08	0.16	0
0.16	0.32	0
0.32	0.64	0
0.64	1.28	1
0.28	0.56	0
0.56	1.12	1
0.12	0.24	0
0.24	0.48	0
0.48	0.96	0
0.96	1.92	1
0.92	1.84	1
0.84	1.68	1
0.68	1.36	1
0.36	0.72	0
0.72	1.44	1
0.44	0.88	0
0.88	1.76	1
0.76	1.52	1

Thus giving 0110000101000111101011.
Note that the pattern would repeat itself since the last row and second row match.