In the IEEE floating point representation, the hexadecimal value 0 × 00000000…
2008
In the IEEE floating point representation, the hexadecimal value 0 × 00000000 corresponds to
- A.
the normalized value 2-127
- B.
the normalized value 2-126
- C.
the normalized value +0
- D.
the special value +0
Attempted by 308 students.
Show answer & explanation
Correct answer: D
Answer: +0 (positive zero)
Interpret the bit pattern 0x00000000 as a 32-bit IEEE 754 single-precision number: all bits are zero → sign = 0, exponent field (8 bits) = 0, fraction (mantissa) = 0.
Rule: If exponent field = 0 and fraction = 0, the encoding denotes a signed zero. The sign bit determines +0 (sign = 0) or -0 (sign = 1).
Normalized numbers require exponent field between 1 and 254 (biased). For single precision the bias is 127, so normalized exponents range from −126 to +127. Subnormal (denormal) numbers have exponent field = 0 and fraction ≠ 0; their values are (−1)^sign × 0.fraction × 2^(−126). The smallest positive subnormal is 2^-149.
Therefore 0x00000000 represents the special value +0, not a normalized value.
A video solution is available for this question — log in and enroll to watch it.