Which of the following statements is/are correct? I. Overflow in two's complement addition can be detected by examining only the…

Question

Which of the following statements is/are correct?

I. Overflow in two's complement addition can be detected by examining only the carry out of the most significant bit.

II. When converting an unsigned integer to a larger type, zero extension is used to preserve its value.

III. In Binary-Coded Decimal (BCD) representation, each decimal digit is encoded separately using four binary bits.

IV. In a byte-addressable system, the effective address calculation is dependent on instruction length.

1. A. Only IV is True
2. B. Only II and III are True (Correct answer)
3. C. Only II and IV are True
4. D. Only III and IV are True

Correct Answer

Option B — B

Detailed Solution & Explanation

The correct answer is Option B.

Key Points

• (Note: the final JKSSB key is B, revised from the provisional C.)
• II is correct: when widening an unsigned integer to a larger type, zero extension (padding with 0s on the left) preserves the value.
• III is correct: in Binary-Coded Decimal (BCD), each decimal digit is encoded separately in four bits (e.g. 25 → 0010 0101).
• I is wrong: two's-complement overflow cannot be detected from the carry-out of the MSB alone; you must compare the carry INTO and carry OUT OF the sign bit.
• IV is wrong: in a byte-addressable system the effective address comes from the addressing mode, and is not simply a function of instruction length.

Exam Tip

• overflow in two's complement = carry-in to the sign bit ≠ carry-out of the sign bit.

Additional Information

• Overflow in two's complement addition is detected when the carry into the sign bit differs from the carry out of it, or equivalently when adding two numbers of the same sign yields the opposite sign.
• Adding numbers of opposite signs can never overflow, which is a useful shortcut when reasoning about such questions.
• Note that JKSSB revised this item from a provisional key of C to a final key of B — always work from the final key when revising.