Octal-to-decimal conversion Interpret 17 (base 8) as an octal number and convert it to decimal (base 10).

Introduction / Context:Octal (base 8) is another positional number system. Although less common today than hexadecimal, it appears in legacy systems and permissions in Unix-like operating systems. Converting small octal numbers to decimal is straightforward and reinforces the concept of place value.

Given Data / Assumptions:

• Octal input: 17₈ (digits allowed 0–7).
• We want the decimal value.
• No fractional part is present.

Concept / Approach:For an octal number d1 d0, the decimal value is d1 * 8^1 + d0 * 8^0. Here, 1 is the “eights” place and 7 is the “ones” place. Ensure digits are within the octal range (0–7); digit 8 would be invalid in octal notation.

Step-by-Step Solution:

Verification / Alternative check:Cross-check via binary: 17₈ = 001 111₂ = 15 decimal, confirming the result.

Why Other Options Are Wrong:

• 51, 57, 82: do not match the correct place-value computation for 17₈.

Common Pitfalls:Interpreting “17” as base 10 or assuming octal digits can include “8” or “9”.

Final Answer:15