FAQs on GATE 2004 ECE Range of signed numbers in 1's complement system

Question 1

1. What is the range of signed numbers in a 1's complement system?

Accepted Answer

Ans. In a 1's complement system, the range of signed numbers is divided into two halves. The positive half ranges from 0 to (2^(n-1)) - 1, where n is the number of bits. The negative half ranges from -1 to -((2^(n-1)) - 1).

Question 2

2. How does the 1's complement system represent negative numbers?

Accepted Answer

Ans. In a 1's complement system, negative numbers are represented by taking the 1's complement of the positive number's binary representation. The 1's complement is obtained by flipping all the bits of the positive number.

Question 3

3. What is the advantage of using a 1's complement system?

Accepted Answer

Ans. One advantage of using a 1's complement system is that it allows for the representation of both positive and negative numbers without the need for a separate sign bit. It simplifies arithmetic operations in some cases as well.

Question 4

4. What is the disadvantage of using a 1's complement system?

Accepted Answer

Ans. One disadvantage of using a 1's complement system is the existence of two representations for zero. Both all 0's and all 1's represent zero, which can introduce ambiguity in certain situations. This ambiguity can affect arithmetic operations and comparisons.

Question 5

5. How does the 1's complement system handle overflow?

Accepted Answer

Ans. In a 1's complement system, overflow occurs when the result of an arithmetic operation exceeds the maximum positive value or falls below the maximum negative value. To handle overflow, the system wraps the result around to the opposite end of the range. For example, if the result exceeds the maximum positive value, it wraps around to the maximum negative value.

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