Non-standard positional numeral systems here designatesnumeral systems that may loosely be described aspositional systems, but that donot entirely comply with the following description of standard positional systems:

In a standard positional numeral system, thebaseb is a positive integer, andb differentnumerals are used to represent allnon-negativeintegers. Each numeral represents one of the values 0, 1, 2, etc., up tob − 1, but the value also depends on the position of thedigit in a number. The value of a digit string likepqrs in baseb is given by thepolynomial form

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

The numbers written in superscript represent thepowers of the base used.

For instance, inhexadecimal (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 aradix point "." and aminus sign "−", allreal numbers can be represented.

• Positional numeral systems