The format of a single-precision floating-point number as per the IEEE 754…
2024
The format of a single-precision floating-point number as per the IEEE 754 standard is:
\(\begin{array}{|c|c|c|} \hline \small \text{Sign} & \small \text{Exponent} & \small \text{Mantissa} \\ \small \text{(1 bit)} & \small \text{(8 bits)} & \small \text{(23 bits)} \\ \hline \end{array} \)
Choose the largest floating-point number among the following options.
- A. SignExponentMantissa00111 11111111 1111 1111 1111 1111 111
- B. SignExponentMantissa01111 11101111 1111 1111 1111 1111 111
- C. SignExponentMantissa01111 11111111 1111 1111 1111 1111 111
- D. SignExponentMantissa00111 11110000 0000 0000 0000 0000 000
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Correct answer: B
Key insight: for normalized single-precision values use value = (−1)^sign × (1 + mantissa/2^23) × 2^(exponent − 127).
Exponent = 11111111 (255) with nonzero mantissa is NaN, not a finite number, so exclude it when choosing the largest finite value.
Exponent = 11111110 (254) with mantissa = all ones yields the largest finite positive value: (2 − 2^−23) × 2^127 ≈ 3.4028235 × 10^38.
Smaller examples: exponent = 01111111 (127) with mantissa all ones gives ≈ 1.99999988, and with mantissa 0 gives 1.0.
Therefore the bit pattern with sign = 0, exponent = 11111110 and mantissa = all ones is the largest finite IEEE 754 single-precision floating-point number.
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