Question 7 of 21intermediate✨ CreateEssay4 marks

Using the ideas discussed in this section, try refining the number system you might have made earlier.

Correct Answer

Key Components of a Refined Number System:

(1) Base System: A base (like 5, 8, or 10) with landmark numbers as powers of the base.

(2) Place Value System: Position determines the power of the base.

(3) Placeholder Symbol: A symbol (like 0) to indicate empty positions.

(4) Limited Symbol Set: Digits from 0 to base-1.

Example — Base-5 System: Symbols: 0, 1, 2, 3, 4 Positions represent: 1, 5, 25, 125, etc.

Conclusion: This allows representing any number unambiguously and enables efficient arithmetic operations.

Exercise: Figure it Out (Section 3) | Q: 4 | (Page Page 14)
For More Understanding

Explanation

The chapter discusses key ideas in number system evolution: counting in groups (like Gumulgal's counting by 2s), using landmark numbers (Roman system), choosing powers of a number as landmark numbers (base systems), and place value representation (Mesopotamian, Mayan, Chinese, Hindu systems). A refined number system should incorporate all these ideas, especially the place value system with a placeholder symbol for 0.

Solution Steps

  1. Choose a base (e.g., 5, 8, or 10) for the number system.

  2. Use powers of the base as landmark numbers.

  3. Implement a place value system where position determines the power.

  4. Include a placeholder symbol (0) for empty positions.

  5. Create a limited set of symbols (digits 0 to base-1).

  6. Verify the system can represent any number unambiguously.

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