Which of the following is not a positional number system?*Roman Number SystemOctal Number SystemBinary Number SystemHexadecimal Number System

Break Down the Problem

1. Identify what constitutes a positional number system.
2. List the given number systems: Roman, Octal, Binary, and Hexadecimal.
3. Determine if each system is positional or not.

Relevant Concepts

A positional number system is one where the value of a digit depends on its position in the number. In contrast, a non-positional number system does not follow this principle.

Analysis and Detail

1. Roman Number System:

   • Utilizes letters to represent values (I, V, X, L, C, D, M).
   • The value is not determined by position; for example, VI (5 + 1) is different from IV (5 - 1).
   • Conclusion: Non-positional.

2. Octal Number System:

   • Base 8 system where each digit represents a power of 8 based on its position.
   • Conclusion: Positional.

3. Binary Number System:

   • Base 2 system where each digit represents a power of 2 based on its position.
   • Conclusion: Positional.

4. Hexadecimal Number System:

   • Base 16 system where each digit represents a power of 16 based on its position.
   • Conclusion: Positional.

Verify and Summarize

After evaluating each system, the Roman Number System does not follow positional principles, while Octal, Binary, and Hexadecimal systems do.

Final Answer

The system that is not a positional number system is the Roman Number System.