GATE 2026 CS (CS2) – Question 34
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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Correct answer: -60.25
Explanation
For `0xC2710000`, the sign bit is 1, so the number is negative. The exponent bits are `10000100`, which is 132 in decimal, so the unbiased exponent is $132-127=5$. The fraction bits correspond to mantissa $1.1110001_2$. Therefore the value is $$-1.1110001_2 \times 2^5 = -111100.01_2 = -60.25.$$ Hence the answer is $-60.25$.