**Non-standard positional numeral systems** here designates numeral systems that may loosely be described as positional systems, but that do * not* entirely comply with the following description of standard positional systems:

- In a standard positional numeral system, the base
*b*is a positive integer, and*b*different numerals are used to represent all non-negative integers. Each numeral represents one of the values 0, 1, 2, etc., up to*b*− 1, but the value also depends on the position of the digit in a number. The value of a digit string like*pqrs*in base*b*is given by the**polynomial form**

- .

- The numbers written in superscript represent the powers of the base used.
- For instance, in hexadecimal (
*b*=16), using the numerals A for 10, B for 11 etc., the digit string 7A3F means- ,

- which written in our normal decimal notation is 31295.
- Upon introducing a radix point "." and a minus sign "−", all real numbers can be represented.