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?
- A.
35C80000
- B.
35CC0000
- C.
35E80000
- D.
35EC0000
Attempted by 44 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