Number system conversion — octal to hexadecimal: Convert the octal number 136₈ to its hexadecimal equivalent and choose the correct answer.

Introduction / Context:
Efficient conversion between octal, binary, and hexadecimal relies on grouping bits because bases 8 and 16 are powers of 2. Octal digits map to 3-bit groups; hexadecimal digits map to 4-bit groups. This allows quick mental or manual conversion without decimal intermediate steps.

Given Data / Assumptions:

• Number to convert: 136₈.
• We aim to produce an exact hexadecimal result.
• No calculators are required; bit grouping is used.

Concept / Approach:
Map each octal digit to a 3-bit binary group, concatenate, then regroup into 4-bit nibbles for hexadecimal. Add leading zeros if necessary to complete the leftmost nibble—this does not change the value.

Step-by-Step Solution:
Write octal to binary: 1 → 001, 3 → 011, 6 → 110.Concatenate: 001 011 110 → binary 001011110.Pad on the left to a multiple of 4 bits: 0000 0101 1110.Translate nibbles: 0000 → 0, 0101 → 5, 1110 → E.Drop leading 0: result = 5E₁₆.

Verification / Alternative check:
Decimal check: 136₈ = 164 + 38 + 6 = 64 + 24 + 6 = 94₁₀. Hex 5E₁₆ = 5*16 + 14 = 80 + 14 = 94₁₀. Matches.

Why Other Options Are Wrong:
7E₁₆ (126₁₀), 5A₁₆ (90₁₀), and 5D₁₆ (93₁₀) do not equal 94₁₀.

Common Pitfalls:
Forgetting to pad the leftmost group to 4 bits or mis-grouping from the right instead of from the left for hex conversion.

Final Answer:
5E₁₆.