Binary arithmetic — addition: Compute 1101₂ + 1010₂ and select the correct binary sum.

Introduction / Context:
Binary addition follows the same carry rules as decimal addition but with base 2 digits. Mastery of bit-wise addition is essential for digital design, arithmetic logic units, and low-level programming.

Given Data / Assumptions:

• Addend A = 1101₂ (decimal 13).
• Addend B = 1010₂ (decimal 10).
• We compute the exact binary sum.

Concept / Approach:
Use columnar addition from least significant bit (rightmost) to most significant bit, carrying when a column sums to 2 (10₂) or 3 (11₂). The process mirrors full-adder logic: sum bit = A ⊕ B ⊕ carry_in, carry_out = majority(A, B, carry_in).

Step-by-Step Solution:
Align bits: 1101 + 1010.LSB: 1 + 0 = 1, carry 0 → sum bit 1.Next: 0 + 1 = 1, carry 0 → sum bit 1.Next: 1 + 0 = 1, carry 0 → sum bit 1.MSB: 1 + 1 = 10₂ → sum bit 0, carry 1.Write final: carry 1 then 0 1 1 1 → 10111₂.

Verification / Alternative check:
Convert to decimal: 13 + 10 = 23. Convert 10111₂ to decimal: 16 + 4 + 2 + 1 = 23. Matches.

Why Other Options Are Wrong:
10101₂ = 21; 11000₂ = 24; 11011₂ = 27; none match 23.

Common Pitfalls:
Forgetting the final carry; misaligning bits when adding numbers of equal length can still produce mistakes if carry is mishandled.

Final Answer:
10111₂.