GATE CS 2026 Set 2 — Question 34
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
The 32-bit IEEE 754 single precision representation of a number is .
The number in decimal representation is ________. (rounded off to two decimal places)
The number in decimal representation is ________. (rounded off to two decimal places)
Correct answer
-60.25
Solution
The hexadecimal representation is .
Converting to binary:Binary string: IEEE 754 Single Precision format (32 bits):
Converting to binary:Binary string: IEEE 754 Single Precision format (32 bits):
- Sign bit (S): 1 bit (MSB)
- Exponent (E): 8 bits
- Mantissa (M): 23 bits
- (Negative number)
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