Consider the following single precision floating point numbers and the operation.
X : (35C00000)H
Y : (34A00000)H
Z =X+Y
What is the value of ’Z’ in hexadecimal?

The correct option is (35E80000)H.

To find the value of $Z=X+Y$ in hexadecimal, we first need to decode the IEEE 754 single-precision floating-point representations of $X$ and $Y$, perform the addition, and then encode the result back into single-precision hexadecimal format.

Step 1: Understand the IEEE 754 Single-Precision Format
A 32-bit single-precision floating-point number is represented as:
- Sign bit (S): 1 bit (MSB)
- Biased Exponent (E): 8 bits
- Mantissa/Fraction (F): 23 bits
The value represented is given by: $(-1{)}^S\times 1.F\times 2^{E-127}$ (for normalized numbers).

Step 2: Decode X = (35C00000)H
Converting the hex value $35C00000$ to binary:
$3\to 0011$
$5\to 0101$
$C\to 1100$
Remaining zeros: $0000...0000$
Thus, the 32-bit binary representation of X is:
$001101011110000000000000000000000$
Grouping into IEEE 754 fields:
- Sign bit ($S_x$): $0$ (Positive number)
- Exponent ($E_x$): $01101011$ in binary = $64+32+8+2+1=107$ in decimal.
- Fraction ($F_x$): $1000000...0$
So, $X=+1.1\times 2^{107-127}=1.1\times 2^{-20}$ in binary.

Step 3: Decode Y = (34A00000)H
Converting the hex value $34A00000$ to binary:
$3\to 0011$
$4\to 0100$
$A\to 1010$
Remaining zeros: $0000...0000$
Thus, the 32-bit binary representation of Y is:
$001101001010000000000000000000000$
Grouping into IEEE 754 fields:
- Sign bit ($S_y$): $0$ (Positive number)
- Exponent ($E_y$): $01101001$ in binary = $64+32+8+1=105$ in decimal.
- Fraction ($F_y$): $0100000...0$
So, $Y=+1.01\times 2^{105-127}=1.01\times 2^{-22}$ in binary.

Step 4: Perform Addition Z = X + Y
To add the two numbers, we align their exponents to the larger exponent, which is $-20$ (from $X$).
We express $Y$ with an exponent of $-20$:
$Y=1.01\times 2^{-22}=0.0101\times 2^{-20}$
Now, add the mantissas:
$Z=(1.1+0.0101)\times 2^{-20}$
$Z=1.1101\times 2^{-20}$

Step 5: Encode Z back to IEEE 754 Single-Precision Format
- Sign bit ($S_z$): $0$ (positive)
- The exponent is $-20$, so the biased exponent is:
$E_z=-20+127=107$ decimal = $01101011$ in binary.
- The mantissa fraction $F_z$ is the fractional part of $1.1101$, which is $1101$ followed by zeros:
$F_z=1101000...0$
Combining the bits:
$00110101111010000000000000000$
Regrouping by 4 bits to convert to hex:
$0011\to 3$
$0101\to 5$
$1110\to E$
$1000\to 8$
$0000\to 0$
$0000\to 0$
$0000\to 0$
$0000\to 0$
This gives: (35E80000)H.