NIMCET 2020
The logic XOR operation of and results
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — FFFF
Detailed Solution
XOR digit by digit in binary: 4 XOR B = 0100 XOR 1011 = 1111 = F.
A XOR 5 = 1010 XOR 0101 = 1111 = F; C XOR 3 = 1100 XOR 0011 = 1111 = F; 0 XOR F = F.
The result is FFFF.
✓ Check
Each digit pair adds up to 15 (4 + 11, 10 + 5, 12 + 3, 0 + 15) with no common 1-bits, so XOR gives F in every place.⚠ Common trap
(B) 0000 would need the two numbers to be equal, since x XOR x = 0.Quick tip
Each digit pair adds to F with no common bits, so 4AC0 XOR B53F = FFFF
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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.