In IEEE floating point representation, the hexadecimal number 0xC0000000…

2017

In IEEE floating point representation, the hexadecimal number 0xC0000000 corresponds to

  1. A.

    -3.0

  2. B.

    -1.0

  3. C.

    -4.0

  4. D.

    -2.0

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Correct answer: D

To convert 0xC0000000 to decimal in IEEE 754 single-precision format, first convert the hexadecimal value to binary: 1100 0000 0000 0000 0000 0000 0000 0000. The first bit is the sign bit (1), indicating a negative number. The next 8 bits represent the exponent: 10000000, which is 128 in decimal. Subtracting the standard bias of 127 yields an actual exponent of 1. The remaining 23 bits are the mantissa, which is all zeros. In normalized form, this implies a significand of 1.0. Therefore, the calculated value is -1.0 multiplied by 2 raised to the power of 1, resulting in exactly -2.0.

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