The question asks to convert the 32-bit IEEE 754 single-precision hexadecimal representation $0xC2710000$ into its decimal equivalent.

Step 1: Convert Hexadecimal to Binary

First, convert the hexadecimal number $0xC2710000$ into its 32-bit binary representation:

• $C$ = $1100$
• $2$ = $0010$
• $7$ = $0111$
• $1$ = $0001$
• $0$ = $0000$

Combining these, the 32-bit binary representation is:

$11000010011100010000000000000000$

Step 2: Identify IEEE 754 Components

For a 32-bit single-precision float, the structure is:

• Sign bit: 1 bit (the most significant bit)
• Exponent bits: 8 bits
• Mantissa bits: 23 bits

Breaking down the binary representation:

• Sign bit (S): $1$
• Exponent bits (E): $10000100$
• Mantissa bits (M): $11100010000000000000000$

Step 3: Interpret the Sign Bit

The sign bit is $1$, which indicates that the number is negative.

Step 4: Interpret the Exponent Bits

The exponent bits are $10000100$.

• Convert this binary exponent to decimal: $(1 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (0 \times 2^0) = 128 + 0 + 0 + 0 + 0 + 4 + 0 + 0 = 132$
• The bias for single-precision floats is 127. Subtract the bias to find the actual exponent value (e): $e = 132 - 127 = 5$

Step 5: Interpret the Mantissa Bits

The mantissa bits are $11100010000000000000000$.

• For normalized numbers (which this is, as the exponent is not all zeros or all ones), there is an implicit leading $1$ before the binary point. The value is represented as $1.M$.
• The binary value is $1.11100010000000000000000_2$.
• Convert the fractional part to decimal: $(1 \times 2^{-1}) + (1 \times 2^{-2}) + (1 \times 2^{-3}) + (0 \times 2^{-4}) + \dots + (1 \times 2^{-7}) + \dots$ $= 0.5 + 0.25 + 0.125 + 0 + \dots + (1/128) + \dots$ $= 0.875 + 0.0078125 = 0.8828125$
• The value represented by the mantissa is $1 + 0.8828125 = 1.8828125$.

Step 6: Calculate the Decimal Value

The formula for the decimal value is $(-1)^S \times (\text{mantissa value}) \times 2^e$.

• Substitute the values: $(-1)^1 \times 1.8828125 \times 2^5$ $= -1 \times 1.8828125 \times 32$ $= -60.25$

The number in decimal representation is $-60.25$. This is already rounded to two decimal places.