Binary subtraction method used in computers: Evaluate the statement: “Digital computers use an easier subtraction method called one's complement.”

Difficulty: Easy

Correct Answer: Incorrect

Explanation:


Introduction / Context:
Modern binary arithmetic for signed integers overwhelmingly uses two's complement. Subtraction A − B is performed as A + (two's complement of B), which unifies add/sub hardware.


Given Data / Assumptions:

  • We consider mainstream digital computers.
  • Signed integer encoding choice impacts subtraction method.


Concept / Approach:
Two's complement of B is formed by bitwise complement (one's complement) plus 1. While one's complement exists historically, it suffers from negative zero and complicates arithmetic. Two's complement removes negative zero and simplifies overflow rules, which is why it is standard.


Step-by-Step Solution:

Identify claim: “one's complement is the easier method.”Recall standard practice: two's complement for subtraction and signed representation.Conclude the statement is incorrect for modern computers.


Verification / Alternative check:
Instruction sets and ALUs implement add with an inverted operand plus one for subtraction, i.e., two's complement.


Why Other Options Are Wrong:

Correct/legacy/toolchain-dependent: Mainstream hardware uses two's complement; one's complement is rare and outdated.Ambiguous sign-magnitude: Not standard for arithmetic units.


Common Pitfalls:
Confusing the intermediate “invert bits” step (one's complement) with the complete two's complement operation.


Final Answer:
Incorrect

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