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

Difficulty: Easy

Correct Answer: 2's-complement system.

Explanation:


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.

More Questions from Digital Arithmetic Operations and Circuits

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion