Terminology — evaluate the statement: “Base is the same as radix.” In number-system language, are the terms “base” and “radix” interchangeable?

Introduction / Context:
In number systems, the size of the digit set and the positional weighting depend on a fundamental parameter often called the “base” or “radix.” Students encounter both terms in digital electronics, computer science, and mathematics. This question clarifies whether the two words are synonymous in this context.

Given Data / Assumptions:

• Digit sets correspond to base b (or radix r), yielding digits 0..b−1.
• Common examples: binary (base/radix 2), octal (8), decimal (10), hexadecimal (16).
• The terms are used in textbooks and standards.

Concept / Approach:
“Base” and “radix” are interchangeable names for the same concept: the number of unique digit symbols and the factor by which place value increases when moving left in a positional numeral system. Each position represents powers of the base/radix: b^0, b^1, b^2, etc. The term “radix” is often used in more formal mathematical or computer-science contexts, but it does not denote a different quantity from “base.”

Step-by-Step Solution:

Verification / Alternative check:
Documentation for programming languages (e.g., integer parsing functions) and mathematics texts routinely use “radix/base” interchangeably when describing conversions and representations.

Why Other Options Are Wrong:

• Incorrect: Contradicts standard usage.
• “Only correct for binary/decimal” or “only in floating-point” adds unnecessary constraints; base/radix applies across all positional systems.

Common Pitfalls:
Confusing “radix point” (generalized decimal point) with the radix value itself; both concepts are related but not identical.

Final Answer:
Correct — “base” and “radix” refer to the same concept in positional number systems.