Question

Three floating point numbers $X, Y,$ and $Z$ are stored in three registers $RX, RY,$ and $RZ,$ respectively, in IEEE 754 single-precision format as given below in hexadecimal: \[ RX = 0xC1100000, \quad RY = 0x40C00000, \quad RZ = 0x41400000 \] Which of the following option(s) is/are CORRECT?

• A. $4(X+Y) + Z = 0$
• B. $2Y - Z = 0$
• C. $4X + 3Z = 0$
• D. $X+Y+Z = 0$

Hint:

IEEE 754 single-precision format uses a 1-bit sign, 8-bit exponent, and 23-bit fraction. Understanding this format helps in decoding floating-point values effectively.

Answer 1

The Correct Option is A, B, C

Using IEEE 754 single-precision floating-point conversion, we decode the given hexadecimal values into their decimal equivalents and verify the given expressions.

By applying the IEEE 754 standard to the given hexadecimal values, we perform the necessary steps to convert them to their respective decimal forms. Once converted, we can evaluate the expressions based on these decimal values.

After computing each expression, we find that options (A), (B), and (C) hold true, as their results match the expected outcomes based on the decoded values.