Binary to Octal Conversion — Grouping by Threes Convert the binary number 001101011 to octal. Choose the correct base 8 representation.

Introduction / Context:Octal conversion is convenient because each octal digit corresponds to three binary bits. Grouping from the right and mapping each triplet eliminates arithmetic and reduces errors during manual conversion.

Given Data / Assumptions:

• Binary: 001101011.
• Octal mapping uses triplets: 000..111 maps to 0..7.
• Pad on the left with zeros to complete a triplet if needed.

Concept / Approach:Partition the binary string into groups of three bits starting at the least significant end, translate each group to its octal digit, and then concatenate in the same order from most significant to least significant group.

Step-by-Step Solution:1) Grouping: 001 101 011.2) Convert each: 001=1, 101=5, 011=3.3) Combine digits: 1 5 3 → 153 base 8.4) Therefore the correct octal form is 153.

Verification / Alternative check:Check by expanding to decimal: 153_8 = 164 + 58 + 3 = 64 + 40 + 3 = 107. Binary 001101011 equals 107 decimal as well, confirming correctness.

Why Other Options Are Wrong:

• 3518, 2538, 3528: These reflect different groupings or digit orderings that do not match the correct triplet mapping.

Common Pitfalls:Grouping from the left instead of the right, or forgetting to pad the leading zeros to complete the most significant triplet.

Final Answer:1538