Base conversion — convert the binary number to octal. Task: Express 101110101111010₂ in octal (group bits in 3s from the right).

Introduction / Context:
Binary-to-octal conversion is efficient because 1 octal digit corresponds to 3 binary bits. Grouping from the right into triads ensures lossless and quick translation, useful for compact human-readable representations of long binary strings.

Given Data / Assumptions:

• Binary: 101110101111010
• No sign or fractional component

Concept / Approach:
Partition the binary string into groups of three bits starting from the right. Convert each 3-bit group to its octal digit (0–7) using the 4-2-1 weights, then concatenate the digits.

Step-by-Step Solution:

Verification / Alternative check:
Convert the octal result back to binary by expanding each digit to 3 bits and confirm it matches the original bit string.

Why Other Options Are Wrong:

• 515628, 565778, 656278, 556728: at least one 3-bit group is misconverted, producing incorrect octal digits.

Common Pitfalls:

• Grouping from the left or forgetting to pad the leftmost group (not needed here as length is already a multiple of 3).

Final Answer:
565728