NIMCET 2026
Consider the following statements about the range of numbers in a 9-bit 1's complement and 2's complement system.I.In 9-bit 1's complement, the range is −255 to +255, and there exist two representations of zero.II.In 9-bit 2's complement, the range is −256 to +255, and both 1's complement and 2's complement can represent exactly 512 unique values.III.The maximum positive number representable is +255 in both 1's complement and 2's complement 9-bit systems.
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Answer: Option C — I and III only
Detailed Solution
I — correct: 1's complement range is to = −255 to +255, with +0 and −0.
II — wrong: the 2's complement range −256 to +255 is right, but 1's complement has only 511 distinct values (two patterns mean 0).
III — correct: the largest positive value is in both systems.
Hence I and III only.
Quick tip
-bit 2's complement: to ; 1's complement:
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Computer Number System — Preparation
This question tests your understanding of Computer Number System, a key topic in the Computer Awareness section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Computers store and process all data in binary, using only the digits 0 and 1. This topic covers the four number systems used in computing: binary (base 2), octal (base 8), decimal (base 10) and hexadecimal (base 16, using digits 0 to 9 and letters A to F). It covers converting numbers between these systems, binary arithmetic (addition, subtraction, multiplication and division), and complements (1's and 2's complement) used to represent negative numbers. The fastest conversions go through binary. Each octal digit equals a group of three binary digits, and each hexadecimal digit equals a group of four. To convert decimal to binary, divide by 2 repeatedly and read the remainders from bottom to top. Character encoding schemes such as ASCII and Unicode are also covered at a basic level. Practise the computer number system questions below, each with a step-by-step conversion.