The following bit pattern represents a floating point number in IEEE 754…

2008

The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is

  1. A.

    -10

  2. B.

    -13

  3. C.

    -26

  4. D.

    None of these

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Correct answer: C

Decode the IEEE 754 single-precision bit pattern 1 10000011 101000000000000000000000:

  • Sign bit = 1 → number is negative.

  • Exponent bits = 10000011₂ = 131. Bias = 127, so exponent = 131 − 127 = 4.

  • Fraction (mantissa) bits = 101000000... → fraction = 1·2⁻¹ + 0·2⁻² + 1·2⁻³ = 0.5 + 0 + 0.125 = 0.625. Significand = 1 + fraction = 1.625.

  • Value = (−1)¹ × 1.625 × 2⁴ = −1.625 × 16 = −26.

Final answer: -26

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