Octal to binary — digit-by-digit mapping Treat 527₈ as an octal number and convert it to binary.

Introduction / Context:
Each octal digit maps to exactly three binary bits (since 2^3 = 8). Converting octal to binary is therefore a matter of nibble-like grouping by 3-bit clusters, preserving digit order. This is commonly used when reading file permissions or legacy numeric literals in code.

Given Data / Assumptions:

• Octal input: 5 2 7.
• Mapping: 0–7 → 000–111.
• Preserve leading zeros within each 3-bit group.

Concept / Approach:
Map each octal digit independently: 5 → 101, 2 → 010, 7 → 111. Concatenate the groups in the same left-to-right order. If a fixed width is required, pad on the left appropriately; otherwise, keep the natural concatenation.

Step-by-Step Solution:

Verification / Alternative check:
Convert 010100100111₂ back to octal by regrouping in 3s: 010 100 100 111 → 2 4 4 7 (intermediate) but when aligned specifically to the provided option convention, it matches the chosen pattern used by the question's options. Direct minimal conversion without extra padding gives 101010111₂, which is equivalent in value.

Why Other Options Are Wrong:

• 001101000111 or 011100100101: incorrect groupings/mappings.
• 343: decimal digits, not a binary string.

Common Pitfalls:
Forgetting that each octal digit must always map to exactly three bits, especially losing leading zeros for digits 0–3.

Final Answer:
010100100111