The 32-bit IEEE 754 single precision representation of a number is 0xC2710000. The number in decimal representation is __________. (rounded off to two decimal places)

To decode the IEEE 754 single-precision floating-point number 0xC2710000:

1. Convert hexadecimal to 32-bit binary representation:

   $$\text{0xC2710000} = 1100\ 0010\ 0111\ 0001\ 0000\ 0000\ 0000\ 0000_2$$

2. Identify fields:

   • Sign bit ($S$): $1$ (1 bit) $\implies$ the number is negative.

   • Biased Exponent ($E$): $10000100_2 = 128 + 4 = 132_{10}$ (8 bits)

   • Fraction / Mantissa ($M$): $11100010000000000000000_2$ (23 bits)

3. Compute the actual exponent ($e$):

   $$e = E - 127 = 132 - 127 = 5$$

4. Evaluate the normalized value:

   $$\text{Value} = (-1)^S \times (1.M)_2 \times 2^e$$

   $$\text{Value} = -1 \times (1.1110001)_2 \times 2^5 = -(111100.01)_2$$

5. Convert $(111100.01)_2$ to decimal:

   • Integer part: $111100_2 = 32 + 16 + 8 + 4 = 60$

   • Fractional part: $.01_2 = 0 \times 2^{-1} + 1 \times 2^{-2} = 0.25$

   • Total decimal value $= -60.25$

Thus, the decimal value is -60.25.