The decimal floating point number −40.1 represented using IEEE-754 32-bit…
2018
The decimal floating point number −40.1 represented using IEEE-754 32-bit representation and written in hexadecimal form is
- A.
0x𝐶2206666
- B.
0x𝐶2206000
- C.
0x𝐶2006666
- D.
0x𝐶2006000
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Correct answer: A
Answer: 0xC2206666
Steps to obtain the IEEE-754 single-precision (32-bit) encoding for -40.1:
Sign bit: 1 (because the number is negative).
Convert the magnitude 40.1 to binary: 40 = 101000. Fraction 0.1 = 0.0001100110011... (repeating pattern 0011). So 40.1 ≈ 101000.0001100110011...
Normalize: 101000.000110011... = 1.010000001100110011... × 2^5. Exponent = 5.
Biased exponent: 127 + 5 = 132 → binary 10000100 (hex 0x84).
Mantissa (fraction) field: Take the bits after the leading 1: 01000000110011001100110 (23 bits, rounded/truncated).
Assemble the 32 bits: sign = 1, exponent = 10000100, mantissa = 01000000110011001100110 → binary 11000010001000000110011001100110.
Convert to hexadecimal: 1100 0010 0010 0000 0110 0110 0110 0110 → 0xC2206666.
Therefore the correct IEEE-754 single-precision hexadecimal representation for -40.1 is 0xC2206666.
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