Match octal numbers to their decimal equivalents: (A) 35₈, (B) 65₈, (C) 54₈, (D) 76₈ — with (1) 53, (2) 62, (3) 29, (4) 44.
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AA-4, B-3, C-2, D-1
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BA-1, B-2, C-3, D-4
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CA-2, B-3, C-1, D-4
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DA-3, B-1, C-4, D-2
Answer
Correct Answer: A-3, B-1, C-4, D-2
Explanation
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:
Compute 35₈: 38 + 5 = 24 + 5 = 29 → (3).Compute 65₈: 68 + 5 = 48 + 5 = 53 → (1).Compute 54₈: 58 + 4 = 40 + 4 = 44 → (4).Compute 76₈: 78 + 6 = 56 + 6 = 62 → (2).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