GATE CS 2026 Set 1 Q.36: ALU, Datapath and Control Unit

Consider the real valued variables $X$ , $Y$ and $Z$ represented using the IEEE 754 single-precision floating-point format. The binary representations of $X$ and $Y$ in hexadecimal notation are as follows:

X: \text{35C00000} \qquad Y: \text{34A00000}

Let $Z = X + Y$ .

Which one of the following is the binary representation of $Z$ , in hexadecimal notation?

35C80000

35CC0000

35E80000

35EC0000

Official answer and solution

Official answer: C
From: Official GATE 2026 answer key

Solution

Unpack the sign, 8-bit biased exponent, and 23-bit mantissa of $X$ and $Y$ , align the smaller exponent to the larger exponent, add the significands, and repack into hexadecimal.

Unpack $X = \text{0x35C00000}$ :
- In binary: 0011 0101 1100 0000 ... $= 0 \mid 01101011 \mid 1000000\dots$
- Sign $S_X = 0$ , biased exponent $E_X = 01101011_2 = 107$ , significand $= 1.1000_2$ .
Unpack $Y = \text{0x34A00000}$ :
- In binary: 0011 0100 1010 0000 ... $= 0 \mid 01101001 \mid 0100000\dots$
- Sign $S_Y = 0$ , biased exponent $E_Y = 01101001_2 = 105$ , significand $= 1.0100_2$ .
Align exponents and add significands:
- Since $E_X - E_Y = 107 - 105 = 2$ , shift $Y$ 's significand right by $2$ bits to match exponent $107$ : $1.0100_2 \times 2^{-2} = 0.0101_2$ .
- Add significands at exponent $E_Z = 107$ : $1.1000_2 + 0.0101_2 = 1.1101_2$
Pack $Z$ into IEEE 754 single-precision format:
- Sign $S_Z = 0$ , biased exponent $E_Z = 01101011_2$ , fraction $= 1101000\dots_2$ : $0\,01101011\,1101000\dots_2 = 0011\,0101\,1110\,1000\,0000\dots_2 = \text{35E80000}_{16}$

Final answer

Option (C)

Common trap

Forgetting the implicit leading 1 of $Y$ 's normalized significand ( $1.01_2$ ) when shifting right by 2 bits.

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

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 36 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