In number systems, the radix (base) of the binary representation is which value?

Introduction / Context:
The concept of a radix, also called a base, is central to understanding how different number systems encode quantities. In positional systems, the radix determines the set of allowed digits and the place-value weights. This question asks for the radix of the binary system, which is the standard language of digital electronics and computing.

Given Data / Assumptions:

• Binary numbers use only two symbols: 0 and 1.
• Each position to the left represents a higher power of the radix.
• We are dealing with unsigned positional notation for clarity.

Concept / Approach:
In any positional system with radix r, the allowed digit symbols run from 0 to r−1, and the positional weights are r^0, r^1, r^2, and so on. Because binary uses two symbols (0 and 1), its radix is 2. Every binary value can be interpreted as a weighted sum of powers of 2, which directly maps to how digital circuits represent and manipulate information using low (0) and high (1) voltage levels.

Step-by-Step Solution:
Identify the symbol set of binary: {0, 1} → two symbols.By definition, the count of distinct digit symbols equals the radix.Therefore, radix = 2.Select option “2.”

Verification / Alternative check:
Compare with decimal (radix 10, digits 0–9) and hexadecimal (radix 16, digits 0–9 and A–F). Binary’s two symbols make its base unambiguously 2.

Why Other Options Are Wrong:
3 would imply digits 0–2; 1 is not a valid radix for positional systems; 10 is the decimal base, not binary; “None of the above” is incorrect because 2 is correct.

Common Pitfalls:
Confusing the number 10 written in binary (which equals 2 decimal) with “base 10”; the string “10” in any base represents the radix value itself, but that does not make the radix 10. Always separate numeral meaning from base identity.

Final Answer:
2