A numeral system is a system for representing numbers based on digits or words. A number is represented according to rules as a sequence of characters, digits or words.
Commonly used are addition systems and positional systems.
In an addition system, a number is represented as the sum of the values of its digits. The position of the individual digits is irrelevant.
An example is the dash system – when something is to be counted. Roman numerals are another example.
In everyday life and in science, a number is usually represented by digits (0, 1, 2, …, 9 and letters (A, B, …). The number of digits used is called the “base of the place value system”. The most common bases are 2 (dual/binary system), 8 (octal system), 10 (decimal system) or 16 (hexadecimal system).
The digits have an order of value determined by convention. When counting up (which corresponds to adding a one), the system moves to the next digit in that order. When adding a one to the most significant digit, the system moves to the least significant digit, and a one is added to the next highest digit.
For this purpose, the digits are evaluated differently depending on their place, where the place value is a power of the base (for example, “ones place”, “tens place”, “hundreds place”, …). The place with the lowest evaluation stands thereby on the right.
The numerical value is then calculated by multiplying the individual digit values by the corresponding place values and adding these products.