Difficulty: Easy
Correct Answer: 110101
Explanation:
Introduction / Context:
Binary addition is foundational for digital logic and computer arithmetic. This problem asks you to convert two decimal values to binary, perform the addition, and express the sum in binary form.
Given Data / Assumptions:
Concept / Approach:
Convert each decimal number to binary, then add the bit patterns using standard binary addition rules (0+0=0, 0+1=1, 1+1=0 with carry 1). Convert back to decimal as a check.
Step-by-Step Solution:
1) Convert 26 to binary: 26 = 16 + 8 + 2 = 11010.2) Convert 27 to binary: 27 = 16 + 8 + 2 + 1 = 11011.3) Add: 11010 + 11011 = 110101.4) Check in decimal: 26 + 27 = 53; 110101 (binary) = 32 + 16 + 4 + 1 = 53. Verified.
Verification / Alternative check:
Use positional weights or quickly re-add in decimal and reconvert: 53 → 32 + 16 + 4 + 1 → 110101. Matches the computed binary sum.
Why Other Options Are Wrong:
111010 (58), 110110 (54), 101011 (43), 100101 (37): all represent incorrect decimal totals for 26 + 27.
Common Pitfalls:
Misplacing carries during addition or mis-conversion between decimal and binary. Writing unequal bit lengths without proper alignment can also cause errors.
Final Answer:
110101
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