How to normalize a mantissa

Question

I\'m trying to convert an int into a custom float, in which the user specifies the amount of bits reserved for the exp and mantissa, but I don\'t understand how

Answer 1

To answer a comment posted on 'how to do this in code': (Assuming it's an IEEE float)

A) Extract an unsigned 'exponent' and 'mantissa' from the IEEE float.

i) exp = 0x7F800000 & yourFloatVar;

//this takes bit b1 through b8 from the float. (b0 is the signed bit, b9 and on is the mantissa)

ii) exp = exp >> 23; //shift right so this exponent is right-oriented

iii) exp += 127; //add in the bias (127 is for 32-bit only)

iv) mantissa = 0x007FFFFF & yourFloatVar; //take last 23 bits from float

B) Normalizing

i)

while(true)
{
    if( ((mantissa & 0xC0000000) != 0x80000000)
         &&((mantissa & 0xC0000000) != 0x40000000) )
    {
        mantissa = mantissa << 1;
        exponent--;
    }
    else //AKA the float has been normalized
    {
        break;
    }
}

if leading 2 bits aren't '01' or '10' (this is a property of 2's complement - the condition to normalize), then shift over the mantissa and decrement the exponent.

I want to note that this isn't at all the most efficient algorithm for doing this; I just wanted to make the steps clear. Hope I didn't miss anything!