Complements — bitwise inversion: What is the 1’s complement (bitwise NOT) of the 16-bit value 0000 1111 0010 1101₂?

Introduction / Context:The 1’s complement of a binary word is formed by inverting each bit: 0 → 1 and 1 → 0. This operation is used in low-level arithmetic, checksum algorithms, and digital logic. Correct grouping into nibbles or bytes helps avoid transcription errors.

Given Data / Assumptions:

• Original word: 0000 1111 0010 1101 (16 bits).
• Operation: bitwise inversion (1’s complement).
• Spacing is only for readability; it does not affect values.

Concept / Approach:Invert each bit independently across all positions. For grouped readability, confirm each nibble inversion using hex if desired: 0x0 → 0xF, 0xF → 0x0, 0x2 → 0xD, 0xD → 0x2. This provides a quick cross-check.

Step-by-Step Solution:Start: 0000 → 1111.Next: 1111 → 0000.Next: 0010 → 1101.Next: 1101 → 0010.Combine: 1111 0000 1101 0010.

Verification / Alternative check:Hex route: 0000 1111 0010 1101₂ = 0x0F2D; 1’s complement → 0xF0D2 → 1111 0000 1101 0010₂. Matches.

Why Other Options Are Wrong:Option A inverts only some nibbles. Options C and D do not correspond to full bitwise inversion of the given word.

Common Pitfalls:Accidentally computing 2’s complement (invert + add 1) instead of 1’s complement; mis-grouping bits when copying.

Final Answer:1111 0000 1101 0010.