Hexadecimal Digits A to F — Decimal Equivalents In hexadecimal notation, the letters A through F correspond to which consecutive decimal values?
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A1 through 6
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B9 through 14
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C10 through 15
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D11 through 17
Answer
Correct Answer: 10 through 15
Explanation
Introduction / Context:Hexadecimal extends decimal digits with letters to represent values ten through fifteen. Knowing these mappings is essential for fast mental conversions and interpreting hex dumps or color codes.
Given Data / Assumptions:
- Base 16 uses symbols 0..9 and A..F.
- Each hex digit represents a 4-bit nibble in binary.
- Letter mapping is standard across computing.
Concept / Approach:Assign A=10, B=11, C=12, D=13, E=14, F=15. This preserves increasing order and provides a compact single digit notation for values beyond 9.
Step-by-Step Solution:1) List the mapping explicitly: A=10, B=11, C=12, D=13, E=14, F=15.2) Observe that these are consecutive decimal numbers.3) Therefore the correct range description is 10 through 15.
Verification / Alternative check:Confirm by checking binary correspondence: for example, F=1111 equals 15 decimal, E=1110 equals 14 decimal, and so on.
Why Other Options Are Wrong:
- 1 through 6: Off by a factor of 9 and not consistent with hex usage.
- 9 through 14: Starts too low and ends too low.
- 11 through 17: Not aligned with base 16 digits, which stop at 15.
Common Pitfalls:Assuming F could mean 16; remember single hex digits only span 0 to 15 inclusive.
Final Answer:10 through 15