Computer Sciences > GATE 2026 SET-2 > Digital Logic
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)
Correct : -60.25
The correct answer is −60.25.
Converting the IEEE 754 single precision hex value 0xC2710000 step by step:
Hex to Binary: 0xC2710000 = 1100 0010 0111 0001 0000 0000 0000 0000
Split the 32 bits into IEEE 754 fields:
Sign bit: 1 (negative number)
Exponent bits: 10000100 = 132 in decimal
Mantissa bits: 11100010000000000000000
Actual exponent: E = 132 − 127 (bias) = 5
Mantissa value (with implicit leading 1):
1.11100010... = 1 + 2−1 + 2−2 + 2−3 + 2−7 = 1 + 0.5 + 0.25 + 0.125 + 0.0078125 = 1.8828125
Final value:
(−1)1 × 1.8828125 × 25 = −1 × 1.8828125 × 32 = −60.25
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