GATE CS 2025 Set 2 Q.49: ALU, Datapath and Control Unit

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:

$R_X = \texttt{0xC1100000}$ , $R_Y = \texttt{0x40C00000}$ , and $R_Z = \texttt{0x41400000}$

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

$4(X + Y) + Z = 0$

$2Y - Z = 0$

$4X + 3Z = 0$

$X + Y + Z = 0$

Official answer and solution

Official answer: A, B and C
From: Official GATE 2025 answer key

Solution

Decode each 32-bit IEEE 754 single-precision hexadecimal value using $(-1)^S \times (1.M)_2 \times 2^{E - 127}$ .

Decoding each 32-bit IEEE 754 single-precision value (1 sign bit $S$ , 8 exponent bits $E$ , 23 fraction bits $M$ ):

$R_X = \texttt{0xC1100000} = \texttt{1 10000010 0010000...}_2$ :
- $S = 1$ , $E = 130 \implies E - 127 = 3$ , $(1.M)_2 = 1.001_2 = 1.125$ .
- $X = -1.125 \times 2^3 = -9$ .
$R_Y = \texttt{0x40C00000} = \texttt{0 10000001 1000000...}_2$ :
- $S = 0$ , $E = 129 \implies E - 127 = 2$ , $(1.M)_2 = 1.1_2 = 1.5$ .
- $Y = +1.5 \times 2^2 = 6$ .
$R_Z = \texttt{0x41400000} = \texttt{0 10000010 1000000...}_2$ :
- $S = 0$ , $E = 130 \implies E - 127 = 3$ , $(1.M)_2 = 1.1_2 = 1.5$ .
- $Z = +1.5 \times 2^3 = 12$ .

Checking each equation for $(X, Y, Z) = (-9, 6, 12)$ :

(A): $4(X + Y) + Z = 4(-9 + 6) + 12 = -12 + 12 = 0$ (TRUE).
(B): $2Y - Z = 2(6) - 12 = 0$ (TRUE).
(C): $4X + 3Z = 4(-9) + 3(12) = -36 + 36 = 0$ (TRUE).
(D): $X + Y + Z = -9 + 6 + 12 = 9 \neq 0$ (FALSE).

Final answer

Options (A), (B), (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 2 (CS2)
Question: 49 of 65
Section: Computer Science and Information Technology

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source