Number-system basics – is hexadecimal a base-4 system?

Introduction / Context:
Digital systems commonly use binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). This question checks if you can recall the correct radix for hex and avoid conflating it with smaller bases like base 4 (quaternary).

Given Data / Assumptions:

• Hexadecimal digits: 0–9 and A–F.
• Each hex digit corresponds to 4 binary bits (a nibble).
• No exotic numbering schemes implied.

Concept / Approach:
Hexadecimal is base 16; each position represents powers of 16. While it maps neatly to binary in 4-bit groups (1 nibble), that convenience does not change the radix. Base 4 would use only digits 0–3 and powers of 4, which is not how hex is defined or used.

Step-by-Step Solution:

Verification / Alternative check:
Convert 0x10 to decimal: 1 * 16 + 0 = 16. If it were base 4, 10_4 equals 4 decimal, which contradicts common usage like memory addresses and hex literals.

Why Other Options Are Wrong:
“Correct” is false. BCD and pairing/grouping practices do not alter radix. Nibble size is fixed at 4 bits because hex is base 16, not the reverse.

Common Pitfalls:
Confusing the 4-bit nibble association with base 4. The nibble-to-hex mapping is about encoding convenience, not radix identity.

Final Answer:
Incorrect