Number systems refresher The base-10 (decimal) number system is composed of how many distinct symbols (digits)?
Correct Answer: 10
Introduction / Context:Understanding different bases is central to digital electronics and computing. Decimal (base 10) is the everyday system; binary (base 2), octal (base 8), and hexadecimal (base 16) are used heavily in engineering. This question checks recall of the decimal system’s symbol count.
Given Data / Assumptions:
- Decimal uses symbols 0 through 9.
- Base b systems use exactly b distinct digit symbols.
- No extended notation (like letters for digits beyond 9) applies to base 10.
Concept / Approach:By definition, a base-10 system has ten unique symbols. Positional notation means each position weight is a power of 10, and digits 0–9 are used to represent quantities at each position.
Step-by-Step Solution:
Recall base-10 digits: 0,1,2,3,4,5,6,7,8,9.Count the set: there are 10 symbols.Match with the option “10.”Confirm other options correspond to bases 2, 8, and 16 respectively.Verification / Alternative check:Conversion methods (e.g., repeated division) and place-value representation rely on exactly ten symbols in decimal arithmetic; elementary math supports this definition unequivocally.
Why Other Options Are Wrong:
- 2: Binary, not decimal.
- 8: Octal, not decimal.
- 16: Hexadecimal, not decimal.
- 20: Not a standard base in common digital practice and certainly not decimal.
Common Pitfalls:Confusing the count of symbols with the largest symbol value; remember the highest digit is 9, but the number of symbols is 10 total.
Final Answer:10