Digital Logic · Number Representation and Arithmetic
Official IIT answer key · IIT Bombay · Audited Aug 2026
GATE CSE 2021 Set 1 Q24 · NAT · 1 mark
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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 →Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. S : 1 E : 10000001 F : 11110000000000000000000 Here S, E and F denote the sign, exponent and fraction components of the floating point representation. The decimal value corresponding to the above representation (rounded to 2 decimal places) is …
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