Identifying the base-16 system: Which named number system uses a radix of sixteen for its digits and is commonly used to compactly represent binary values?

Introduction / Context:
Number systems with different bases are used in electronics and computing for convenience and clarity. Hexadecimal is especially useful because each digit maps to exactly four binary bits. This question checks your understanding of which named system corresponds to base sixteen (radix 16).

Given Data / Assumptions:

• Base sixteen implies 16 distinct digit symbols.
• In hex, symbols are 0–9 and A–F.
• Binary is base two, octal is base eight.

Concept / Approach:
Match the given bases to their conventional names: binary → base 2, octal → base 8, hexadecimal → base 16. Johnson is not a number system; it typically refers to a Johnson counter in digital design, unrelated to radix notation.

Step-by-Step Solution:

Verification / Alternative check:
Consider conversion: 0xFF maps to binary 1111 1111, clearly demonstrating the 4-bits-per-digit relationship.

Why Other Options Are Wrong:
Johnson is not a radix system; binary is base 2; octal is base 8.

Common Pitfalls:
Confusing device names or counter types with number systems; mixing up octal and hexadecimal bases.

Final Answer:
hexadecimal