Two’s complement arithmetic: Using the two’s complement system, we can add numbers of any sign (including like signs) with the same adder hardware and obtain a correct signed result when interpreted in two’s complement.

Introduction / Context:
Two’s complement is the dominant signed-integer format in processors because a single binary adder can handle both addition and subtraction. The claim is that adding numbers with like signs works correctly in this system. In fact, two’s complement supports addition for both like and unlike signs seamlessly.

Given Data / Assumptions:

• Operands are represented in two’s complement using a fixed width (n bits).
• We use standard binary addition; overflow is detected by carry into/out of the sign bit mismatch.
• Results are interpreted in the same width (mod 2^n arithmetic).

Concept / Approach:
Two’s complement encodes negative x as 2^n − |x|. A single binary adder can add any two n-bit patterns and produce a correct two’s complement result, with overflow indicated when the carries into and out of the MSB differ. Like-sign addition is no exception; the arithmetic is uniform.

Step-by-Step Solution:

Verification / Alternative check:
Example with 8 bits: 0010 0101 (+37) + 0000 1011 (+11) = 0011 0000 (+48) — correct. With negatives, 1110 1101 (−19) + 1111 1001 (−7) = 1100 0110 (−58) — correct, no extra hardware.

Why Other Options Are Wrong:
Limiting correctness to positive operands or to sign–magnitude ignores the key advantage of two’s complement: uniform addition for all signs.

Common Pitfalls:
Confusing carry-out with overflow; in two’s complement overflow is not the same as a simple carry.

Final Answer:
Correct