In positional numeral systems used for digital electronics, the hexadecimal digit set extends from 0–9 and A through which final letter?

Difficulty: Easy

Correct Answer: F

Explanation:


Introduction / Context:
Hexadecimal (base 16) is widely used to concisely express binary values, since each hex digit represents exactly 4 bits. Knowing the exact digit range is foundational for reading memory dumps and configuring low-level systems.


Given Data / Assumptions:

  • Hexadecimal base is 16.
  • Decimal digits cover 0–9; additional symbols map to 10–15.
  • Letters A–F represent 10–15 respectively.


Concept / Approach:
The hex sequence is {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}. Therefore, the final letter in the sequence is F. This mapping directly aligns with 4-bit binary: 0000 to 1111 equals 0 to F.


Step-by-Step Solution:

Count symbols: 10 numerals + 6 letters = 16 unique digits.Map letters to decimals: A=10, B=11, C=12, D=13, E=14, F=15.Therefore, the last hex letter is F.


Verification / Alternative check:
Any standard ASCII/Unicode table and programming language formatters (e.g., printf %X) confirm that hex digits end at F.


Why Other Options Are Wrong:

  • E: second-to-last; equals decimal 14.
  • G: not a valid hex digit.
  • D: equals decimal 13; not the final letter.
  • None of the above: incorrect because F is correct.


Common Pitfalls:
Confusing base-16 with base-14 or assuming letters continue beyond F; misreading lowercase vs uppercase (both are accepted, but the set still ends at F).


Final Answer:
F

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