Jamia Millia Islamia MCA 2017
The 2's complement of the binary number is
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Answer: Option A — 1001100
Detailed Solution
1's complement (invert every bit): 0110100 becomes 1001011.
Add 1: 1001011 + 1 = 1001100.
✓ Check
0110100 + 1001100 = 10000000; dropping the carry leaves 0000000, as a number plus its 2's complement must.⚠ Common trap
(D) 1101011 looks like the 1's complement 1001011 with one bit flipped; the 2's complement also needs the +1 of Step 2.Quick tip
Copy bits from the right up to the first 1, invert the rest: 0110|100 to 1001|100
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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.