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Number system basics: How many distinct digits are available in the octal (base-8) numeral system?

Difficulty: Easy

Correct Answer: 8

Explanation:

Introduction / Context:
This question checks fundamental knowledge of number systems, which are the basis of digital logic and computer arithmetic. Octal is often used as a compact representation of binary values.

Given Data / Assumptions:

Octal system: base-8.
Digits range from 0 up to one less than the base.

Concept / Approach:
In any base-N system, the number of available digits is N, ranging from 0 to N−1. For octal, base = 8 ⇒ digits = {0,1,2,3,4,5,6,7}. That makes exactly 8 distinct digits.

Step-by-Step Solution:

Octal base = 8.Digits are 0 through 7.Count them: 8 digits total.

Verification / Alternative check:

Compare with decimal (base 10 → 10 digits: 0–9), binary (base 2 → digits: 0,1).

Why Other Options Are Wrong:

7: would omit one digit; incorrect.9 or 10: correspond to base-9 or base-10, not base-8.16: corresponds to hexadecimal, not octal.

Common Pitfalls:

Confusing 'base' with 'highest digit' (highest digit is base−1, but number of digits is base).

Number system basics: How many distinct digits are available in the octal (base-8) numeral system?

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