Non-standard positional numeral systems

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

${\displaystyle p\times b^{3}+q\times b^{2}+r\times b+s}$.

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

${\displaystyle 7\times 16^{3}+10\times 16^{2}+3\times 16+15}$,

which written in our normal decimal notation is 31295.

Upon introducing a radix point "." and a minus sign "−", all real numbers can be represented.