Base conversion — convert the octal number to decimal. Task: Find the decimal value of 74₈ by expanding with powers of 8.

Introduction / Context:Octal (base 8) is often used as a compact representation of binary. Converting octal to decimal reinforces understanding of positional weights based on powers of 8.

Given Data / Assumptions:

• Octal number: 74₈
• Digits: 7 and 4 (valid octal digits 0–7)

Concept / Approach:Expand using positional weights: the left digit is multiplied by 8^1 and the right digit by 8^0, then sum the results to get the decimal value.

Step-by-Step Solution:

Verification / Alternative check:Convert 74₈ to binary: 7 → 111, 4 → 100; combined 111100₂ = 60₁₀, confirming the same result.

Why Other Options Are Wrong:

• 74: confuses the symbol with its base-10 interpretation.
• 22, 62, 58: incorrect arithmetic of octal expansion.

Common Pitfalls:

• Including digits 8 or 9 in octal or misapplying decimal weights instead of powers of 8.

Final Answer:60