Match octal numbers to their decimal equivalents: (A) 35₈, (B) 65₈, (C) 54₈, (D) 76₈ — with (1) 53, (2) 62, (3) 29, (4) 44.

Introduction:
Base conversion is foundational in digital systems. This problem reinforces converting from octal (base 8) to decimal (base 10) using positional weights.

Given Data / Assumptions:

• Digits are 0–7 in octal.
• Weighting: the rightmost digit has weight 8^0 = 1, next is 8^1 = 8, etc.
• Target decimal values: 29, 53, 44, 62.

Concept / Approach:

For a two-digit octal ab₈, decimal value is a8 + b. Apply the same logic digit-wise for longer numbers using powers of 8.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check by reversing: 29 → 83 + 5 (digits within 0–7), etc., confirming valid octal representations.

Why Other Options Are Wrong:

Any mismatch indicates arithmetic or base-weighting errors (e.g., using base 10 weights).

Common Pitfalls:

Using base-10 weights; allowing digits 8 or 9 in octal; swapping digit order when multiplying by 8.

Final Answer:

A-3, B-1, C-4, D-2