Question

In two's complement representation, which statement is true?

• A. The MSB (Most Significant Bit) is always 0
• B. The MSB determines the sign of the number
• C. Addition does not require special handling
• D. Two's complement is not used in modern computers

Hint:

To find the two's complement of a binary number, you can use the invert and add one method. Flip all the bits (0s become 1s and 1s become 0s), and then add 1 to the result.

Answer 1

The Correct Option is B

Two's complement is the standard method used by most computers to represent signed integers.
Let's analyze the statements:
(A) The MSB (Most Significant Bit) is always 0: This is incorrect. The MSB is 0 for positive numbers and 1 for negative numbers.
(B) The MSB determines the sign of the number: This is true. The MSB acts as the sign bit. If the MSB is 0, the number is positive or zero. If the MSB is 1, the number is negative.
(C) Addition does not require special handling: While two's complement arithmetic simplifies addition and subtraction into a single addition operation, overflow conditions must still be handled. So, this statement is not entirely true in all contexts. Compared to (B), (B) is a more fundamental and universally true statement about the representation itself. The primary reason for the discrepancy with the provided key (B) is likely due to the ambiguity of special handling. The key advantage is that the same hardware can perform addition on both signed and unsigned numbers, which is a form of 'not requiring special handling'. However, the answer key provided in the PDF is (B). A possible reason the key points to (B) is that the core algorithm for addition (binary addition) works for both positive and negative numbers without change, which is a key advantage. Let's re-evaluate. The question may have a flaw. If we must choose, the fact that the MSB determines the sign is the most definitive true statement about the representation. The statement about addition is a property of its use, and could be debated. The provided answer key is B, and it is a correct statement.
(D) Two's complement is not used in modern computers: This is false. It is the most widely used system for signed integer arithmetic in modern computers.
Reconsidering the PDF key: The provided key is (B). The statement The MSB determines the sign of the number is a fundamental and correct property of two's complement representation. The statement Addition does not require special handling is also a major benefit but can be seen as less precise. Given the options, (B) is an unequivocally true statement.