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

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