The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable $X$ is assigned the decimal value of $-14.25$. The representation of $X$ in hexadecimal notation is

To convert the decimal number $-14.25$ into IEEE-754 32-bit single-precision floating-point format:

1. Sign bit ($S$): Since the number is negative, $S = 1$.

2. Binary Conversion:

   • Integer part: $14_{10} = 1110_2$

   • Fractional part: $0.25_{10} = 0.01_2$

   • Thus, $14.25_{10} = 1110.01_2$

3. Normalized Scientific Notation:

   $$1110.01_2 = 1.11001_2 \times 2^3$$

   • Exponent $E = 3$

   • Mantissa (fractional part) $M = 11001_2$

4. Biased Exponent:

   $$\text{Biased Exponent} = E + 127 = 3 + 127 = 130_{10} = 10000010_2$$

5. Mantissa Field (23 bits):

   $$M = 11001000000000000000000_2$$

6. Combine all fields:

   • Sign (1 bit): 1

   • Biased Exponent (8 bits): 10000010

   • Mantissa (23 bits): 11001000000000000000000

   Grouping into 4-bit nibbles:

   $$\underbrace{1100}_{\text{C}} \quad \underbrace{0001}_{1} \quad \underbrace{0110}_{6} \quad \underbrace{0100}_{4} \quad \underbrace{0000}_{0} \quad \underbrace{0000}_{0} \quad \underbrace{0000}_{0} \quad \underbrace{0000}_{0}$$

7. Hexadecimal Representation:

   $$\text{C1640000H}$$

Therefore, option (A) is the correct answer.