Binary arithmetic — multi-operand addition: Compute the sum of the five binary numbers 110101101₂, 111011101₂, 000111111₂, 100101101₂, and 111110111₂. Choose the correct final binary sum.

Introduction / Context:
Adding multiple binary numbers follows the same column-wise procedure as decimal addition, with carries propagated when a column sum reaches 2 or more. Accuracy benefits from aligning bit widths and verifying with a decimal cross-check.

Given Data / Assumptions:

• Numbers: 110101101₂, 111011101₂, 000111111₂, 100101101₂, 111110111₂.
• All are 9-bit values; pad if needed for alignment.
• We will compute the exact sum and validate against the options.

Concept / Approach:
Perform column addition from LSB to MSB, or convert to decimal to confirm. Carry out careful arithmetic to avoid bit slips. The final binary result must match one of the answer choices to be correct; otherwise “None of the above” applies.

Step-by-Step Solution:
Convert each to decimal for a reliable check: 110101101₂=429, 111011101₂=477, 000111111₂=63, 100101101₂=301, 111110111₂=503.Add: 429 + 477 = 906.906 + 63 = 969.969 + 301 = 1270.1270 + 503 = 1773 (decimal total).Convert 1773 back to binary: 1773₁₀ = 11011101101₂.

Verification / Alternative check:
Column-wise binary addition yields the same result 11011101101₂. Comparing with provided options shows none match 11011101101₂, hence “None of the above.”

Why Other Options Are Wrong:
Each listed binary choice corresponds to decimal values far from 1773; for example, 1011010111010₂=5818, 1111011000010₂=7874, etc., so they cannot be correct.

Common Pitfalls:
Mistyping bits, forgetting carries, or misaligning numbers. Always double-check with a decimal round-trip when possible.

Final Answer:
None of the above.