NIMCET 2011
When two binary numbers are added, an overflow will never occur if
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — the carry into the sign bit position and the carry out of the sign bit position are equal
Detailed Solution
In signed (2's complement) addition, overflow occurs exactly when the carry into the sign bit differs from the carry out of the sign bit.
So when the two carries are equal, overflow never occurs.
✓ Check
In 4 bits, : the carry into the sign bit is and out is , and gives , an overflow. : both carries are , and is correct.⚠ Common trap
Option (A) is wrong: overflow can happen only when both numbers have the same sign, as in above.Quick tip
Overflow at the sign bit; equal carries mean no overflow
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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.