The range of representable normalized numbers in the floating point binary…
2014
The range of representable normalized numbers in the floating point binary fractional representation in a 32-bit word with 1-bit sign, 8-bit excess 128 biased exponent and 23-bit mantissa is
- A.
2⁻¹²⁸ to (1 − 2⁻²³) × 2¹²⁷
- B.
(1 − 2⁻²³) × 2⁻¹²⁷ to 2¹²⁸
- C.
(1 − 2⁻²³) × 2⁻¹²⁷ to 2²³
- D.
2⁻¹²⁹ to (1 − 2⁻²³) × 2¹²⁷
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Correct answer: A
Exponent field = 8 bits, bias = 128
For normalized numbers, the smallest stored exponent is 1
Actual minimum exponent = 1 − 128 = −127
Smallest normalized value = 1.0 × 2⁻¹²⁷
With binary fractional representation, the minimum magnitude is written as 2⁻¹²⁸
Largest normalized value occurs when mantissa is all 1s:
(1 − 2⁻²³) × 2¹²⁷
👉 Therefore, the correct range is:
2⁻¹²⁸ to (1 − 2⁻²³) × 2¹²⁷
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