In digital number systems, convert the decimal value 13 (base 10) to its equivalent in octal (base 8), ensuring correct place-value interpretation and without skipping intermediate steps.

Introduction / Context:Base conversion is a core digital logic skill. This question asks you to convert a decimal value (base 10) to octal (base 8) using repeated division by the target base and reading remainders in reverse order.

Given Data / Assumptions:

• Given number: 13 in base 10.
• Target base: 8 (octal).
• No fractional part; only integer conversion is required.

Concept / Approach:The standard approach converts from base 10 to base b by repeatedly dividing the number by b and collecting remainders. The octal representation is built by reading the remainders from last to first.

Step-by-Step Solution:

Verification / Alternative check:Use place-value back-conversion: 15₈ → 1*8 + 5 = 13 (base 10). Matches the original value, confirming accuracy.

Why Other Options Are Wrong:

• 17₈: equals 1*8 + 7 = 15, not 13.
• 13₈: equals 1*8 + 3 = 11, not 13.
• 11₈: equals 8 + 1 = 9, not 13.
• None of the above: incorrect because 15₈ is correct.

Common Pitfalls:Reading remainders in the wrong order, mixing decimal digits as if they were octal digits, or forgetting to stop when the quotient becomes 0.

Final Answer:15₈