Two’s-complement arithmetic is the standard method used by general-purpose computer systems and processors to perform signed integer addition and subtraction. Evaluate this statement.

Introduction / Context:Two’s-complement encoding enables the same adder circuitry to handle both positive and negative integers, simplifying hardware and enabling efficient arithmetic. It is pervasive across ISAs and microarchitectures.

Given Data / Assumptions:

• We discuss signed integer arithmetic on typical CPUs and controllers.
• Objective is to represent negative values and perform addition/subtraction efficiently.
• Overflow detection follows two’s-complement rules.

Concept / Approach:Two’s complement represents −x as (~x) + 1. Using this scheme, subtraction A − B becomes A + (~B + 1), so a single binary adder suffices for addition and subtraction. Sign bit participates naturally in the addition, avoiding special sign handling required by sign-magnitude or one’s-complement schemes.

Step-by-Step Solution:1) Encode negatives by inversion plus 1.2) Perform A − B as A + (two’s-complement of B).3) Use overflow rules: for addition, overflow occurs when adding two numbers with the same sign produces a result with the opposite sign.4) Hardware uses the same adder for both operations, minimizing complexity.

Verification / Alternative check:Survey architectures (x86, ARM, RISC-V, MIPS); all use two’s complement for signed integers.

Why Other Options Are Wrong:“Incorrect” contradicts standard practice. “Only for floating-point” is wrong—floating point uses IEEE-754, not two’s complement. “Replaced by sign-magnitude” is historically reversed.

Common Pitfalls:Confusing encoding for integers with floating-point formats; misapplying overflow rules across representations.

Final Answer:Correct