Fractional binary number for given hexadecimal representation:

• From the given question, the binary value for given hexadecimal is "0x40490FDB" is "0100 0000 0100 1001 0000 1111 1101 1011".
• Using the single precision floating point approximation, the bit of "sign" is "1", for exponent bit "k" is "8" and for fraction bits is "23".
• Hence, the floating point representation for given binary value is

• From the above table, it is based on the normalized case.
  • Because, the value of exponent is not all zeros. Then formula for computing "E", "M" and "V" is
    • Formula for computing "E", "E = e – bias"
    • Formula for computing "M", "M = 1 + f"
    • Formula for computing "V", "V=(−1)s×ばつ2E×ばつM"
• From the above table, sign bit "s" is "0".

E=e−bias=128−bias=>Computingdecimalvalueforexponentbit"10000000"is128=128−(28−1−1)=>Formuladeterminebiasis2k−1−1

Fractional binary representation of "227":

From problem 2.83, assume n = 0.yyyyyy. So, from part A, n=11.001 001 000 011 111 101 101 1 . Hence, the value of "y" is "001".

Now formula to computing numeric value for string "001" is given below

n=Y2k−1

Here the value of "Y" means decimal value for "001" and "k" means number of bits in given binary "001"

Bit positions of "π" diverge from two approximations:

Relative to the binary point, at the 9^th bit position, the "π" diverges from two approximations of "22371" and "227".

• When converting "22371" to decimal, the value is "3