Number Systems

A number system is a writing system for expressing numbers, using a specific set of digits or symbols according to consistent rules. The core principle of modern systems is the base, or radix, which determines the number of unique digits and the value of each position (place value). While the decimal (base-10) system is ubiquitous in daily life, other systems are vital in specific domains, most notably the binary (base-2) system that forms the foundation of all digital computing, as well as hexadecimal (base-16) used in programming and computer engineering.

1. Introduction to Number Systems
   1. Definition of Number Systems
   2. Core Concepts
      1. Digit
      2. Symbol
      3. Base (Radix)
      4. Place Value
      5. Notation
   3. Classification of Number Systems
      1. Positional Systems
         1. Definition and Characteristics
         2. Place Value Principle
      2. Non-Positional Systems
         1. Definition and Characteristics
         2. Additive Principle
   4. Historical Development
      1. Early Counting Methods
      2. Development of Written Numerals
      3. Cultural Influences on Number Systems
      4. Evolution to Positional Systems