In positional numeral systems used for digital electronics, the hexadecimal digit set extends from 0–9 and A through which final letter?
-
AE
-
BF
-
CG
-
DD
-
ENone of the above
Answer
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