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GATE 2025 CS (CS2) – Question 49

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

Three floating point numbers $X, Y$, and $Z$ are stored in three registers $R_X$, $R_Y$, and $R_Z$, respectively in IEEE 754 single precision format as given below in hexadecimal:

$R_X$ = 0xC1100000, $R_Y$ = 0x40C00000, and $R_Z$ = 0x41400000

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

  1. $4(X + Y) + Z = 0$
  2. $2Y - Z = 0$
  3. $4X + 3Z = 0$
  4. $X + Y + Z = 0$

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Show answer and explanation

Correct answer: (A) $4(X + Y) + Z = 0$; (B) $2Y - Z = 0$; (C) $4X + 3Z = 0$

Explanation

Decoding gives X = -9, Y = 6, Z = 12. Then 4(-3)+12 = 0, 2·6-12 = 0 and 4(-9)+3(12) = 0, while X+Y+Z = 9.