Number systems: The radix of a positional numeral system is defined as what—specifically with respect to how many distinct symbols the system uses for counting digits (e.g., binary, octal, decimal, hexadecimal)?

Introduction / Context:
Every positional numeral system is characterized by a base, also called the radix. Knowing the radix explains digit ranges, place values, and why the same quantity needs different numbers of digits in different systems (for example, 255 is FF in hexadecimal but 11111111 in binary).

Given Data / Assumptions:

• We are discussing positional systems such as base-2, base-8, base-10, and base-16.
• We seek the precise definition of radix.

Concept / Approach:

The radix is the number of distinct symbols available for a single digit, including zero. Decimal has 10 symbols (0–9), so its radix is 10; binary has 2 symbols (0–1), radix 2; hexadecimal has 16 symbols (0–9 and A–F), radix 16. Place values are powers of the radix: base^0, base^1, base^2, and so on.

Step-by-Step Solution:

Verification / Alternative check:

Check examples: In octal (radix 8), the largest single digit is 7 and each place represents 8^k; in hexadecimal (radix 16), the largest single digit is F (15), each place is 16^k—confirming the definition.

Why Other Options Are Wrong:

• 'Has nothing to do with digit position value': false; place values are powers of the radix.
• 'Is always an even number': false; decimal 10 is even, but base 3 or base 5 are common odd radices.
• 'Is variable': vague and untrue as a definition.
• None: incorrect because the correct definition is provided.

Common Pitfalls:

• Confusing 'radix' with 'radian' (an angle unit). The proper term here is radix.

Final Answer:

Equals the number of its distinct counting digits.