Compute the 2's complement of the 16-bit binary word 0011 0101 1001 1100 and report the result as grouped bits.

Introduction / Context:
Two’s complement is the dominant representation for signed integers in computer systems. It enables straightforward addition/subtraction using the same binary adder hardware. Converting a positive binary word to its two’s complement negative (or vice versa) uses a simple invert-plus-one recipe.

Given Data / Assumptions:

• Original 16-bit word: 0011 0101 1001 1100.
• Spaces are visual groupings; they do not affect bit values.
• We apply the standard 2’s complement operation.

Concept / Approach:

The two’s complement of a binary word W is computed by inverting every bit (forming the one’s complement) and then adding 1 to the result. This effectively computes 2^n − W for an n-bit word, which represents the arithmetic negation modulo 2^n.

Step-by-Step Solution:

Verification / Alternative check:

Hex cross-check: 0011 0101 1001 1100 = 0x359C; two’s complement = 0xCA64. Adding 0x359C + 0xCA64 = 0x10000 (overflow ignored in 16 bits), confirming correctness.

Why Other Options Are Wrong:

Options a, b, and d differ by one or more bits; none equals the computed sum after the +1 step. Therefore option c is the unique correct result.

Common Pitfalls:

Forgetting the +1 after inversion, mishandling carries across grouped spaces, or inverting only up to the first 1 from the right (which is an alternative shortcut but easy to misapply).

Final Answer:

1100 1010 0110 0100