Digital Logic · Number Representation and Arithmetic
Official IIT answer key · IIT Kharagpur · Audited Aug 2026
GATE CSE 2014 Set 2 Q45 · MCQ · 2 marks
float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −14.25. The representation of X in hexadecimal notation isKey concept
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Topic notes
Number representation and arithmetic in GATE CS tests a student's precise understanding of positional number systems, fixed-point signed representations (2's complement, 1's complement, sign-magnitude), and IEEE 754 floating-point standards. Questions consistently balance direct conversions, range and boundary condition calculations, and arithmetic overflow detection across single and multi-register operations. Recent years exhibit a marked transition toward testing multi-register algebraic relationships and MSQ-based overflow condition checking.
Full Number Representation and Arithmetic guide →The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of -14.25. The representation of X in hexadecimal notation is
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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.