Octal to Decimal — Positional Evaluation Convert the octal number 35 (base 8) to its decimal equivalent. Show the weighted sum explicitly.

Introduction / Context:
Converting from octal to decimal uses positional weights that are powers of eight. This reinforces the general positional numeral system concept used across all bases.

Given Data / Assumptions:

• Octal number: 35_8.
• Digit positions from right: 8^0, 8^1, 8^2, and so on.
• Digits are valid octal symbols 0..7.

Concept / Approach:
Multiply each digit by its positional weight and add. The rightmost digit multiplies by 8^0 = 1, the next by 8^1 = 8, and so forth.

Step-by-Step Solution:
1) Write 35_8 as 38^1 + 58^0.2) Compute weights: 8^1 = 8, 8^0 = 1.3) Evaluate: 38 = 24; 51 = 5.4) Sum: 24 + 5 = 29 decimal.

Verification / Alternative check:
Convert 29 back to octal by repeated division by 8: 29 / 8 = 3 remainder 5, reconstructing 35_8.

Why Other Options Are Wrong:

• 71 and 92: Values inconsistent with the small range of two octal digits.
• 17: Result of misplacing digit weights or treating the number as base 10.

Common Pitfalls:
Confusing base when evaluating weights, or reading 35 as thirty five decimal instead of base 8 representation.

Final Answer:
29