Three floating point numbers 𝑋, π‘Œ, and 𝑍 are stored in three registers RX,…

2025

Three floating point numbers 𝑋, π‘Œ, and 𝑍 are stored in three registers RX, RY, and RZ, respectively in IEEE 754 single precision format as given below in hexadecimal:

RX = 0xC1100000, RY = 0x40C00000, and RZ = 0x41400000

Which of the following option(s) is/are CORRECT?

  1. A.

    4(𝑋 + π‘Œ) + 𝑍 = 0

  2. B.

    2π‘Œ – 𝑍 = 0

  3. C.

    4𝑋 + 3𝑍 = 0

  4. D.

    𝑋 + π‘Œ + 𝑍 = 0

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Correct answer: A, B, C

Convert the hex values to decimal (IEEE 754 single precision):

  • RX = 0xC1100000 β†’ -9.0

  • RY = 0x40C00000 β†’ 6.0

  • RZ = 0x41400000 β†’ 12.0

Evaluate each equation using X = -9.0, Y = 6.0, Z = 12.0:

  • 4(X + Y) + Z = 4(-9 + 6) + 12 = 4(-3) + 12 = -12 + 12 = 0 β†’ holds.

  • 2Y βˆ’ Z = 2 * 6 βˆ’ 12 = 12 βˆ’ 12 = 0 β†’ holds.

  • 4X + 3Z = 4 * (-9) + 3 * 12 = -36 + 36 = 0 β†’ holds.

  • X + Y + Z = -9 + 6 + 12 = 9 β‰  0 β†’ does not hold.

Final answer:

The equations that evaluate to zero are 4(X + Y) + Z = 0, 2Y βˆ’ Z = 0, and 4X + 3Z = 0.

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