Binary numeral system: how many symbols are there? Evaluate the statement: “In a binary system there are only two symbols.” Decide whether this description of the base-2 numeral system is accurate.

Introduction / Context:Positional numeral systems are characterized by their base (radix) and the number of distinct digit symbols. Binary is base-2 and is the foundation of digital electronics. This item tests recognition of a fundamental property of the binary system.

Given Data / Assumptions:

• Binary digits (bits) are the atomic symbols used in base-2 numeration.
• Digital logic encodes these symbols as valid LOW and HIGH levels.
• No special coding (e.g., Gray, BCD) alters the number of symbols of the base itself.

Concept / Approach:By definition, a base-r system uses r unique digit symbols. For base-2, r = 2, hence two symbols. In digital practice these symbols are represented by two valid voltage/current ranges. All binary numbers, signed or unsigned, are sequences of these two symbols, even if interpreted differently by higher-level formats.

Step-by-Step Solution:

Verification / Alternative check:Compare with other bases: octal (8 symbols 0–7), decimal (10 symbols 0–9), hexadecimal (16 symbols 0–9 and A–F).

Why Other Options Are Wrong:

Common Pitfalls:Confusing encoding schemes (e.g., BCD, Gray) with the underlying base; these are alternative mappings built from the same two symbols.

Final Answer:Correct