Number systems — hexadecimal base identification In positional numeral systems, what is the base (radix) used by the hexadecimal system?

Difficulty: Easy

Correct Answer: sixteen.

Explanation:


Introduction / Context:
Hexadecimal (often shortened to “hex”) is widely used in digital electronics and computer systems because it maps neatly to binary. Understanding bases (also called radices) helps you convert between binary, decimal, octal, and hex, and to read memory dumps, color codes, and instruction encodings.


Given Data / Assumptions:

  • The question asks for the base of the hexadecimal system.
  • Hexadecimal digits run from 0 to F inclusive.
  • Each hex digit corresponds exactly to four binary bits.


Concept / Approach:
In any base-b system, the allowed digits are 0 through (b − 1). Hexadecimal provides 16 distinct symbols: 0–9 for zero through nine, and A–F for ten through fifteen. Therefore, the radix is 16. This base is convenient because grouping binary bits in sets of four converts directly to one hex digit.


Step-by-Step Solution:

1) List hex symbols: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.2) Count symbols: 16 distinct values.3) By definition, the count of symbols equals the base.4) Hence, hex is base 16 (sixteen).


Verification / Alternative check:
Check binary grouping: 1 hex digit ↔ 4 bits. For example, 0xA = 1010₂. This one-to-one nibble mapping confirms base 16 usage in practice.


Why Other Options Are Wrong:

  • Two: base 2 is binary.
  • Ten: base 10 is decimal.
  • Eight: base 8 is octal.


Common Pitfalls:
Confusing hex with decimal because both use digits 0–9; hex additionally uses A–F.


Final Answer:
sixteen.

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion