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Octal number system — Confirm or refute: “The octal system consists of eight digits, 0 through 7.”

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction / Context:
Number systems specify the base (radix) and the set of digits used. Octal has radix 8, which means each digit place represents a power of 8 and valid digit symbols are 0–7. This question tests recognition of the basic definition of octal.

Given Data / Assumptions:

  • Base b number systems use digits 0 to b−1.
  • Octal’s base is 8, hence 8 distinct digit symbols.
  • Octal historically mapped well to 3-bit binary groups (since 8 = 2^3).


Concept / Approach:
Each position in an octal numeral has weight 8^n. Converting between octal and binary is straightforward via 3-bit groupings, which made octal popular on early minicomputers with 12- or 24-bit words. While hex later became standard, the digit set remains 0–7 by definition.

Step-by-Step Solution:

Identify radix r = 8.Confirm allowed digits are 0 through r−1 → 0–7.Conclude the statement matches the formal definition.


Verification / Alternative check:

Convert an octal value to binary by replacing each digit with its 3-bit equivalent (e.g., 7_o → 111_b).


Why Other Options Are Wrong:

Incorrect: Conflicts with the radix rule.True only for floating-point octal: Floating-point does not change the digit set.Depends on encoding scheme: Encoding of symbols is separate from the mathematical digit set.


Common Pitfalls:

Including digits 8 or 9, which are invalid in octal.Mixing octal notation with decimal values without a prefix/suffix.


Final Answer:

Correct
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