Signed number representation — most common method Which signed-binary representation is most commonly used in digital systems for arithmetic?

Introduction / Context:Storing negative numbers in binary requires a signed representation. Hardware designers overwhelmingly choose one approach because it simplifies arithmetic and hardware implementation. This question asks you to identify that dominant choice.

Given Data / Assumptions:

• Target: general-purpose CPUs, microcontrollers, DSPs.
• Requirements: efficient addition/subtraction, unique zero, straightforward overflow behavior.

Concept / Approach:2's-complement provides a single representation for zero, simple subtraction by addition of complements, and the same adder hardware for signed and unsigned arithmetic. 1's-complement has two zeros; sign-magnitude complicates arithmetic with separate sign handling. 10's-complement is for decimal systems, not binary hardware.

Step-by-Step Solution:Compare properties: unique zero, simple adder reuse → 2's-complement excels.Note disadvantages in alternatives: two zeros in 1's-complement; sign-magnitude requires extra sign logic.Hence, the most common method is 2's-complement.

Verification / Alternative check:ISA specifications (e.g., x86, ARM, RISC-V) and compiler assumptions confirm 2's-complement as the de facto standard for signed integers.

Why Other Options Are Wrong:

• 1's-complement: dual zeros and end-around carry complexity.
• 10's-complement: decimal-specific, not binary hardware.
• Sign-magnitude: inefficient arithmetic and two sign cases.

Common Pitfalls:

• Confusing the 2's-complement operation with bitwise NOT (which is 1's-complement).
• Forgetting that range is asymmetric (one extra negative value) in 2's-complement.

Final Answer:2's-complement system.