In digital number systems, convert the decimal value 13 (base 10) to its equivalent in octal (base 8), ensuring correct place-value interpretation and without skipping intermediate steps.
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A15₈
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B17₈
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C13₈
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D11₈
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ENone of the above
Answer
Correct Answer: 15₈
Explanation
Introduction / Context:Base conversion is a core digital logic skill. This question asks you to convert a decimal value (base 10) to octal (base 8) using repeated division by the target base and reading remainders in reverse order.
Given Data / Assumptions:
- Given number: 13 in base 10.
- Target base: 8 (octal).
- No fractional part; only integer conversion is required.
Concept / Approach:The standard approach converts from base 10 to base b by repeatedly dividing the number by b and collecting remainders. The octal representation is built by reading the remainders from last to first.
Step-by-Step Solution:
Let N = 13 (base 10), base = 8.Step 1: 13 / 8 = quotient 1, remainder 5.Step 2: 1 / 8 = quotient 0, remainder 1.Read remainders upward (last to first): 1 then 5 → 15 in base 8.Check: 1*8^1 + 5*8^0 = 8 + 5 = 13, correct.Verification / Alternative check:Use place-value back-conversion: 15₈ → 1*8 + 5 = 13 (base 10). Matches the original value, confirming accuracy.
Why Other Options Are Wrong:
- 17₈: equals 1*8 + 7 = 15, not 13.
- 13₈: equals 1*8 + 3 = 11, not 13.
- 11₈: equals 8 + 1 = 9, not 13.
- None of the above: incorrect because 15₈ is correct.
Common Pitfalls:Reading remainders in the wrong order, mixing decimal digits as if they were octal digits, or forgetting to stop when the quotient becomes 0.
Final Answer:15₈