The 32-bit IEEE 754 single precision representation of a number is 0xC2710000. The number in decimal

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Question

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)

Accepted Answer

Answer: -60.25Concept -- IEEE 754 Single-Precision Decoding: 0xC2710000 = 1100 0010 0111 0001 0000 0000 0000 0000 in binary. Bits: sign=1 (negative), exponent bits=10000100 (binary) = 132 decimal. Exponent = 132 - 127 = 5. Mantissa bits = 11100010000000000000000 (23 bits). The implicit leading 1 gives significand = 1.1110001 (binary). 1.1110001₂ = 1 + 1/2 + 1/4 + 1/8 + 0/16 + 0/32 + 0/64 + 1/128 = 1 + 0.5 + 0.25 + 0.125 + 0.0078125 = 1.8828125. Multiply by 2^5 = 32 gives 60.25. With sign negative → -60.25.Alternative method: 0xC2710000 = 0xC271 Note: IEEE 754 single precision: 1 sign bit, 8 exponent bits (bias 127), 23 fraction bits. To convert, extract components, compute value = (-1)^s × 1.fraction × 2^(exponent-127).

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)

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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)

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More Questions from Number Representations (Fixed and Floating Point)

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