A positional representation system is a mathematical notation method used to express numbers by assigning meaning to the digits' positions within a number. In this system, the position of each digit determines its value, and the entire value of the number is established by the combination of these positional values.
One of the most widely used positional representation systems is the decimal system, also known as the base-10 system. In this system, each digit's value is determined by its position, and the base value is 10. For instance, in the number 358, the digit '3' represents 300 (3 multiplied by 10²), the digit '5' represents 50 (5 multiplied by 10¹), and the digit '8' represents 8 (8 multiplied by 10⁰). Adding these positional values together results in the total value of 358.
Positional representation systems can also utilize various bases, such as binary (base-2), hexadecimal (base-16), or even non-integer bases. In binary, for example, only two digits (0 and 1) are used, and the base value is 2. This means that the position of each digit represents a power of 2. Similarly, in hexadecimal, 16 digits (0-9 and A-F) are used, and the base value is 16, with each position representing a power of 16.
The advantage of positional representation systems is their ability to represent numbers of any magnitude or precision effectively. By assigning meaning to each digit's position, these systems allow for efficient and intuitive mathematical calculations and manipulations.
