The 32-bit IEEE 754 single precision representation of a number is: 0xC2710000…

Step-by-Step Conversion

The given 32-bit IEEE 754 single precision hexadecimal value is 0xC2710000.

First, convert the hexadecimal value to binary:

C = 1100, 2 = 0010, 7 = 0111, 1 = 0001, 0 = 0000, 0 = 0000, 0 = 0000, 0 = 0000

Binary: 1100 0010 0111 0001 0000 0000 0000 0000

Break down the 32 bits into Sign (1 bit), Exponent (8 bits), and Mantissa (23 bits):

Sign bit: 1 (Negative number)

Exponent bits: 10000100

Mantissa bits: 11100010000000000000000

Calculate the actual exponent:

Exponent (binary) = 10000100 = 128 + 4 = 132

Actual Exponent = 132 - 127 (bias) = 5

Calculate the significand (Mantissa + 1):

Mantissa = 1.1110001 (binary)

Convert to decimal: 1 + 1/2 + 1/4 + 1/8 + 1/128 = 1 + 0.5 + 0.25 + 0.125 + 0.0078125 = 1.8828125

Final Calculation:

Value = (-1)^Sign × Significand × 2^Actual Exponent

Value = -1 × 1.8828125 × 2^5

Value = -1 × 1.8828125 × 32

Value = -60.25

The decimal representation rounded to two decimal places is -60.25.