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GATE CSE 2026 Session 1 Q36: IEEE 754 single-precision sum of 35C00000 and 34A00000

Question

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: 35C00000 \qquad Y: 34A00000

Let Z=X+YZ = X + Y.

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

Try it: multiple choice: exactly one correct option

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Wrong answer costs 2/3 mark in GATE.
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Answer: C (official GATE 2026 final answer key)

Concept used: Floating-point addition: decode sign, biased exponent and significand, align exponents, add, renormalise.

First step: Decode X=1.12×2−20X = 1.1_2 \times 2^{-20} (exponent field 107) and Y=1.012×2−22Y = 1.01_2 \times 2^{-22} (exponent field 105), then shift YY right by 2 bits.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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