Two’s-complement transformation Determine the two’s-complement of each 5-bit binary number: 00110, 00011, 11101. Provide all three results in order.

Difficulty: Medium

Correct Answer: 11010 11101 00011

Explanation:


Introduction / Context:
Two’s-complement conversion is fundamental for signed arithmetic. Applying it correctly requires inverting bits and adding one, and doing so at a fixed bit-width (here, 5 bits).



Given Data / Assumptions:

  • Bit-width: 5 bits for each number.
  • Numbers: 00110, 00011, 11101.
  • Find each number’s two’s complement.


Concept / Approach:
Two’s-complement of an n-bit value X is defined as (~X + 1) with operations constrained to n bits. For a positive X, this yields its negative; for an already negative pattern, it returns the positive magnitude.



Step-by-Step Solution:
For 00110: invert → 11001; add 1 → 11010.For 00011: invert → 11100; add 1 → 11101.For 11101: invert → 00010; add 1 → 00011.


Verification / Alternative check:
Add each original to its two’s complement (mod 5-bit) → result should be 00000 with a discarded carry, confirming correctness.



Why Other Options Are Wrong:
Other sequences reflect missing the +1 step, using one’s complement instead, or mixing bit widths.


Common Pitfalls:
Forgetting to limit to 5 bits after addition or performing complement on fewer/more bits than specified.



Final Answer:
11010 11101 00011

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