Hexadecimal base identification: Does the hexadecimal numbering system use base 15, or is it defined as a base-16 system with digits 0–9 and A–F?

Introduction / Context:
Number systems are characterized by their base (radix), which determines how many distinct digit symbols can appear in any position. This question checks whether hexadecimal is base 15 or base 16 and reinforces the digit set used for hex representation in digital systems.

Given Data / Assumptions:

• Hexadecimal is commonly used to compress binary notation.
• The digits used in hex are 0–9 followed by letters A–F.
• Each hex digit corresponds to exactly 4 binary bits.

Concept / Approach:
Because hexadecimal has 16 distinct symbols, its base is 16. The mapping to binary is 1 hex digit ↔ 4 bits since 16 = 2^4. A base-15 system would only have 15 symbols and would not align with a 4-bit grouping. Using letters does not change the base; it simply provides symbols for values 10–15.

Step-by-Step Solution:

Verification / Alternative check:
Convert a binary nibble like 1010 to hex A; this validates the 4-bit ↔ 1 hex digit mapping that depends on base 16.

Why Other Options Are Wrong:
Endianness affects byte order, not radix; “base 12 if letters are used” is arbitrary; base 10 with letter aliases would be decimal, which it is not.

Common Pitfalls:
Confusing symbol choices with base; thinking that the presence of letters implies a different numbering base.

Final Answer:
Incorrect