Octal to decimal conversion: Convert the octal number 63₈ to its decimal value.

Introduction / Context:
Octal (base-8) to decimal (base-10) conversion is straightforward using positional weights of powers of 8. This is a common skill in digital systems where octal and hexadecimal provide compact representations of binary values.

Given Data / Assumptions:

• Octal input: 63₈.
• We seek the exact decimal value.
• Digits are valid octal digits (0–7).

Concept / Approach:
For a two-digit octal ab₈, the decimal value is a8 + b. Apply positional weights: the left digit has weight 8^1 = 8; the right digit has weight 8^0 = 1.

Step-by-Step Solution:
Compute: 68 + 3 = 48 + 3 = 51.Therefore, 63₈ = 51₁₀.

Verification / Alternative check:
Binary route: 6 → 110, 3 → 011; 110011₂ = 51₁₀ as 32 + 16 + 3 = 51. Matches.

Why Other Options Are Wrong:
61₁₀, 57₁₀, and 53₁₀ correspond to other octal inputs; they do not match 63₈.

Common Pitfalls:
Mixing octal with decimal arithmetic or misreading the base subscript.

Final Answer:
51₁₀.