Number systems refresher: The term 'base 10' refers to which positional number system that uses digits 0 through 9?

Introduction / Context:
Different number systems are used in computing and electronics for convenience: decimal for human interaction, binary for machine-level representation, octal and hexadecimal for compact notation. Understanding the base of a system clarifies how place values work and how to convert between representations.

Given Data / Assumptions:

• Base is the count of unique digit symbols before carry occurs.
• We compare common systems: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).
• Binary-coded decimal (BCD) is an encoding of decimal digits using binary, not a separate base.

Concept / Approach:
Base 10 means each place value represents a power of 10. Digits 0–9 are valid symbols. When a column exceeds 9, a carry is propagated to the next higher place value, which is weighted by an additional factor of 10. This positional structure is the familiar decimal system used in everyday arithmetic.

Step-by-Step Solution:

Verification / Alternative check:
Try representing a number such as 347 in base 10: 310^2 + 410^1 + 7*10^0. This confirms the positional meaning of base 10 and distinguishes it from other bases which would use different weights.

Why Other Options Are Wrong:

• Binary coded decimal: An encoding scheme for decimal digits, not a different base.
• Octal: Base 8 uses digits 0–7 and weights 8^n.
• Hexadecimal: Base 16 uses digits 0–9 and A–F with weights 16^n.

Common Pitfalls:
Confusing BCD with a number base, and assuming that a different symbol set automatically implies a different base. The base is defined by the count of symbols and the positional weights, not the physical encoding.

Final Answer:
decimal