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

  1. A.

    the normalized value 2-127

  2. B.

    the normalized value 2-126

  3. C.

    the normalized value +0 

  4. D.

    the special value +0 

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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.

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