By definition, a positional number system with base r uses exactly r distinct digit symbols. These symbols typically range from 0 to r - 1. The base describes how many unique values a single digit can take. Therefore, r symbols are necessary and sufficient to represent numbers in that base.
Option A:
Option A is correct because the base and the number of symbols are conceptually linked. In base 10 we use 10 symbols, and in base 2 we use 2 symbols. This pattern generalises to base r requiring r symbols.
Option B:
Option B suggests r - 1 symbols, which would only cover values from 0 to r - 2. This would leave one value unrepresented and break the completeness of the system.
Option C:
Option C proposes r + 1 symbols, which would introduce redundancy beyond what is required by the base. Having more symbols than the base allows would complicate representations unnecessarily.
Option D:
Option D indicates 2r symbols, again providing many more symbols than required by the base. This would not align with standard definitions of positional number systems.
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