Binary arithmetic — find the 2's complement of the 8-bit value. Task: Determine the 2's complement of 11100111₂ (invert bits and add 1).

Introduction / Context:
The 2's complement operation is the standard way to represent negative numbers and to perform subtraction on binary systems. It is computed by inverting all bits (1's complement) and then adding 1 to the result.

Given Data / Assumptions:

• Original 8-bit value: 11100111
• Unsigned bitwise operations; no sign extension beyond 8 bits

Concept / Approach:
Two steps: first invert each bit; second add 1 while staying within 8 bits (discard any carry beyond bit 7).

Step-by-Step Solution:

Verification / Alternative check:
To verify, add the original and its 2's complement: 11100111 + 00011001 = 1 00000000 (carry out ignored), confirming correctness under 8-bit arithmetic.

Why Other Options Are Wrong:

• 11100110: only subtracts 1 instead of forming 2's complement properly.
• 00011000: that is the 1's complement, not 2's complement.
• 00011010: off by one from the correct 2's complement.
• 11111001: unrelated bit pattern for this operation.

Common Pitfalls:

• Forgetting to add 1 after inversion, or performing addition with more than 8 bits without discarding the final carry.

Final Answer:
00011001