Floating point

Question

The decimal equivalents of $01440000$ a $32$- bit hexadecimal representation of $IEEE$ single-precision floating point number is

1. $1.11 \times 2^{-125}$
2. $1.88 \times 2^{-125}$
3. $1.68 \times 2^{-124}$
4. $1.88 \times 2^{-129}$

Comments

None of These…………...

Answer 1

01440000

0|000 0001 0|100 0100 0000 0000 0000 0000

1st bit sign = +ve

next 8 bits - x-cess 127 bias so exponent = 2-127 =-125

mantissa 100 01 = (1.10001) = (1+1/2+1/32)=49/32= 1.53 

1.53125 * 2^-125

Comments

There is no closest option - all options are wrong here and your answer is correct. 

#include<stdio.h>
#include<math.h>
int main()

{
        float a = 1.53125 * powf(2, -125);
        char c[2], d;
        int i, h;
        for(i = 0; i < 4; i++)
        {
                d = *((char*) &a + 3 - i); //taking first byte on little endian
                c[0] = (d & 0xf0 ) >> 4; //taking top half of byte
                c[1] = d & 0x0f; //taking lower half of the byte
                printf("%0X%0X", c[0], c[1]);
        }
        printf("\n");
}
$ ./a.out
01440000