Question

Here is a formula that says how the three fields of IEEE 754 combine to represent a number: value = (-1)^s × 1.M × 2^E-127

s is the sign bit, M is the mantissa (with the leading 1 assumed) and E is the biased exponent.

What biased exponent would be used to represent 2^-3?

Write the answer 8 bits.

Answer 1

number = 2^-3

E-127 = -3

E = -3+127 = 124

let's convert 124 to binary

Divide 124 successively by 2 until the quotient is 0
       > 124/2 = 62, remainder is 0
       > 62/2 = 31, remainder is 0
       > 31/2 = 15, remainder is 1
       > 15/2 = 7, remainder is 1
       > 7/2 = 3, remainder is 1
       > 3/2 = 1, remainder is 1
       > 1/2 = 0, remainder is 1

so, biased exponent is 1111100

Answer: 01111100