Binary addition practice: Add decimal 26 and 27 in binary and choose the correct binary sum.

Introduction / Context:
Converting between decimal and binary and then performing binary addition reinforces number-system fluency vital for digital logic, encoding, and low-level software work.

Given Data / Assumptions:

• Operands: 26 and 27 (decimal).
• Required: binary sum.

Concept / Approach:
Convert each decimal number to binary, perform column-wise binary addition with carries, and then confirm by reconverting the result back to decimal.

Step-by-Step Solution:

Verification / Alternative check:
Decimal calculation confirms 53. Long addition in binary shows carries from lower bits forming the sixth bit in the result, which is expected for sums exceeding 31.

Why Other Options Are Wrong:

• 111010 (58), 110110 (54), 101011 (43): Do not equal 53; arithmetic mismatch.

Common Pitfalls:
Dropping a carry when adding the least significant bits; mis-conversion of decimal to binary (especially around the 16 and 8 positions).

Final Answer:
110101