Hexadecimal digit count: How many distinct symbol positions are required to represent all digits in the base-16 (hexadecimal) number system?

Introduction / Context: Hexadecimal (base 16) is widely used in digital electronics as a compact way to represent binary numbers. Each hexadecimal digit maps exactly to a 4-bit binary nibble. This question tests basic understanding of the radix and the number of distinct symbols that a base requires.

Given Data / Assumptions:

• The radix is 16.
• Digits for hex are conventionally written as 0–9 and A–F.
• Each unique digit symbol represents a distinct value from 0 up to base − 1.

Concept / Approach: In any base-R system, there are R unique digit symbols. Therefore, base 16 requires 16 symbols. Hexadecimal uses 10 numeric digits (0–9) for values 0 through 9 and 6 alphabetic symbols (A–F) for values 10 through 15. This mapping aligns perfectly with 4-bit binary groups since 16 = 2^4.

Step-by-Step Solution:

Verification / Alternative check: Map a binary nibble to a hex symbol: for example, 1111 maps to F (value 15). The existence of F confirms the need for 16 distinct symbols (0 through 15 inclusive).

Why Other Options Are Wrong: Six or ten would correspond to bases 6 or 10; twelve is base 12 and does not match 4-bit grouping; none match base 16.

Common Pitfalls: Confusing the number of symbols with the largest symbol value; misremembering that A–F correspond to 10–15, not 11–16.

Final Answer: Sixteen