Consider the real valued variables X, Y and Z represented using the IEEE 754…

2026

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 Y: 34A00000

Let 𝑍 = 𝑋+𝑌.

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

Answer: C. 35E80000 — Step 1: Convert Hexadecimal to BinaryConvert X and Y from hexadecimal to 32-bit binary representation. X: 35C00000 -> 0011 0101 1100 0000 0000 0000 0000 0000…

  1. A.

    35C80000

  2. B.

    35CC0000

  3. C.

    35E80000

  4. D.

    35EC0000

Attempted by 65 students.

Show answer & explanation

Correct answer: C

Step 1: Convert Hexadecimal to Binary

Convert X and Y from hexadecimal to 32-bit binary representation.

X: 35C00000 -> 0011 0101 1100 0000 0000 0000 0000 0000

Y: 34A00000 -> 0011 0100 1010 0000 0000 0000 0000 0000

Step 2: Parse IEEE 754 Fields

X: Sign=0, Exponent=01101011 (107), Mantissa=1.1000...

Y: Sign=0, Exponent=01101001 (105), Mantissa=1.0100...

Step 3: Align Exponents

Difference in exponents is 2. Shift Y's mantissa right by 2 bits.

Y Mantissa becomes 0.010100... (aligned to exponent 107)

Step 4: Add Mantissas

Add X and aligned Y mantissas: 1.1000... + 0.010100... = 1.110100...

Step 5: Convert Result to Hex

Result Binary: 0011 0101 1110 1000 0000 0000 0000 0000

Hexadecimal: 35E80000

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