Consider the following representation of a number in IEEE 754 single-precision…
2021
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.
S : 1 E : 10000001 F : 11110000000000000000000Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation.
The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.
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Correct answer: -7.75
Answer: -7.75 (rounded to 2 decimal places)
Sign (S): 1, so the number is negative.
Exponent (E): 10000001₂ = 129. Unbiased exponent = 129 − 127 = 2.
Fraction (F): 0.111100000...₂ = 2⁻¹ + 2⁻² + 2⁻³ + 2⁻⁴ = 0.5 + 0.25 + 0.125 + 0.0625 = 0.9375.
Significand (mantissa) = 1 + 0.9375 = 1.9375.
Value = (−1) × 1.9375 × 2² = −1.9375 × 4 = −7.75.
Rounded to two decimal places: −7.75.