Question

For IEEE 754 single-precision floating point, what is the hexadecimal representation of 27.101562?

A. 35CCD001

B. 2F5C10D0

C. 41D8D000

D. 7DCA1111

E. None of the above

Answer 1

What is the hexadecimal representation of 27.101562 in IEEE 754 single-precision floating point standard:

Answer: (C) 41D8D000

Description:

• IEEE 754 single-precision floating point representation:

(1) Sign field:

The sign of mantissa will be 0 if the given number is positive and 1 if the given number is negative.

(2) Exponent field:

For getting the stored exponent field, a bias (i.e. 127 for single point precision) will be added to actual exponent.

(3) Mantissa field:

The mantissa is significant digits that is an actual numeric part in scientific notation or in a floating-point number. Normalized mantissa contains only single 1 on the left side of the decimal point. (e.g. 1.00001000000010100000000)

• Representing 27.101562 to IEEE 754 single-precision floating point:

• Given number is positive. So, sign = 0

27 = 11011

0.101562 = 0.0001101 (rounded)

27.101562 = 11011.0001101

11011.0001101 = 1.10110001101 x 2⁴

• Biased exponent = 127 + 4 = 131 = 10000011

• Mantissa: 10110001101000000000000 (fill remaining bits with 0 to complete 23 bits)

(1.10110001101 x 2⁴ : take the part after decimal point and add the rest 0's to make it of 23 bits)

• Binary: 01000001110110001101000000000000

• Hexadecimal: 41D8D000