Base conversion: Convert the binary number 101110₂ to its octal equivalent and select the correct result.

Introduction / Context:
Converting between binary and octal is efficient because octal is a power-of-two base. Each octal digit corresponds to exactly three binary bits, enabling quick grouping without intermediate decimal steps. This is a staple skill in digital electronics and computer architecture courses.

Given Data / Assumptions:

• Binary value: 101110₂.
• Goal: express it in octal (base-8).
• Method: group bits into 3-bit chunks from the right.

Concept / Approach:
Binary to octal mapping is: 000→0, 001→1, 010→2, 011→3, 100→4, 101→5, 110→6, 111→7. Group the binary number into triads, padding the leftmost group with leading zeros if necessary; then translate each triad directly to an octal digit.

Step-by-Step Solution:
Write 101110₂ and group from the right: 101 110.Convert: 101₂ → 5₈; 110₂ → 6₈.Concatenate octal digits: 56₈.

Verification / Alternative check:
Decimal cross-check: 101110₂ = 32 + 8 + 4 + 2 = 46₁₀. Octal 56₈ = 5*8 + 6 = 40 + 6 = 46₁₀. Values match, confirming the conversion.

Why Other Options Are Wrong:
35₈ converts to 29₁₀; 46₈ equals 38₁₀; 50₈ equals 40₁₀—none equal 46₁₀.

Common Pitfalls:
Grouping from the left instead of the right or forgetting to pad leading zeros can yield incorrect digit boundaries. Always group 3 bits per octal digit starting at the LSB side.

Final Answer:
56₈.