Given the following binary number in 32-bit (single precision) IEEE-754 format…
2017
Given the following binary number in 32-bit (single precision) IEEE-754 format :
00111110011011010000000000000000
The decimal value closest to this floating-point number is :
- A.
1.45 X 101
- B.
1.45 X 10-1
- C.
2.27 X 10-1
- D.
2.27 X 101
Attempted by 145 students.
Show answer & explanation
Correct answer: C
Key steps: convert the sign, exponent, and mantissa and compute the value.
Sign bit: 0 → positive.
Exponent bits: 01111100 (binary) = 124 (decimal). Exponent E = 124 − 127 = −3.
Mantissa bits: 11011010000000000000000 → fraction = 0.8515625, so significand = 1.8515625.
Value = (+)1.8515625 × 2^−3 = 1.8515625 / 8 = 0.2314453125 ≈ 2.31 × 10^−1.
Conclusion: The converted value is about 0.23145, so the given choices, the closest is 2.27 X 10 -1 (≈ 0.227).
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