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
- A.
-10
- B.
-13
- C.
-26
- 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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