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GATE 2023 CS – Question 45

Computer Organization and Architecture · Number Representation and Floating Point Arithmetic · 2 marks · Multiple choice

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4. Which one of the following corresponds to the product of these numbers (i.e., P × Q), represented in the IEEE-754 single precision format?

  1. 0x404C2EF4
  2. 0x405C2EF4
  3. 0xC15C2EF4
  4. 0xC14C2EF4

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Correct answer: (C) 0xC15C2EF4

Explanation

P = −1.0 × 2⁴ (sign 1, exponent 131). Q = 1.36… × 2⁻¹ (exponent 126, mantissa 5C2EF4). The product has sign 1, exponent 4−1+127 = 130 (0x82) and the same mantissa, giving 0xC15C2EF4.