In number systems used in computer science and digital electronics, what is the base (radix) of the octal numeral system?

Introduction / Context:
Numeral systems are ways of writing and working with numbers using different bases. While chemistry is the listed category, many competitive exams also test basic computer awareness and number systems. The octal system, along with binary and hexadecimal, is used in computer science and digital electronics because it provides a compact way to represent binary numbers. This question asks for the base, also called the radix, of the octal numeral system, which means the number of distinct digits and the value on which place values are based.

Given Data / Assumptions:

• The numeral system in question is the octal system.
• In any positional numeral system, the base or radix determines the number of digits and their place values.
• The options include 2, 8, 16, 32 and 64, which are all powers of 2 often seen in computing contexts.
• We assume the standard definition of octal used in mathematics and computer science.

Concept / Approach:
The name of a numeral system usually hints at its base. For example, binary has base 2, decimal has base 10 and hexadecimal has base 16. The prefix octa indicates eight, so the octal system uses base 8. This means it uses eight digits, from 0 to 7, and each place value represents a power of 8, such as 8^0, 8^1, 8^2 and so on. When you count in octal, after 7 you carry over to the next place, just as after 9 you carry over in decimal. Therefore, the correct base of the octal system is 8.

Step-by-Step Solution:
Step 1: Recognise that the word octal comes from the Latin root for eight, similar to octagon meaning eight sided polygon. Step 2: In a positional numeral system with base 8, the allowed digits are 0, 1, 2, 3, 4, 5, 6 and 7, which are eight distinct digits. Step 3: Each position in an octal number represents a power of 8, such as units, eights, sixty fours and so on. Step 4: Because of this, the radix or base of the octal system is 8. Step 5: Bases 2, 16, 32 and 64 correspond to binary, hexadecimal and other higher radices used in special contexts, not to standard octal. Step 6: Therefore, among the choices given, 8 is the correct base of the octal numeral system.

Verification / Alternative check:
Converting between binary and octal is often done by grouping binary digits in sets of three because 2^3 is 8. Each group of three binary digits corresponds to one octal digit, which is strong evidence that the base is 8. Computer architecture materials and programming textbooks consistently define octal numbers as base 8 and show digits only from 0 to 7 in valid octal literals. This consistency across different learning resources verifies that the octal numeral system has base 8 and not any other value listed in the options.

Why Other Options Are Wrong:
Option B, 16, is the base of the hexadecimal system, which uses digits 0 to 9 and letters A to F. Option C, 32, and option D, 64, are higher bases sometimes used in specialised encoding schemes but are not standard names in everyday number system questions. Option E, 2, is the base of the binary system, the fundamental language of digital circuits. None of these match the definition of octal, which by its name and usage is always base 8. Only option A is correct.

Common Pitfalls:
Students sometimes confuse octal with hexadecimal because both are used alongside binary in computing. Another pitfall is to focus on powers of 2 and guess that the base must be a higher power like 16 or 32. To avoid such errors, remember the simple mapping: binary base 2, octal base 8, decimal base 10 and hexadecimal base 16. Keeping this small set of associations in mind will help you quickly answer many number system questions in exams without overthinking them.

Final Answer:
The base or radix of the octal numeral system is 8.