There are many different numeral systems, that is, writing systems for expressing numbers.

By culture / time period

By type of notation

Numeral systems are classified here as to whether they use

positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...

(also known as place-value notation), and further categorized by

radix In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is t ...

or base.

Standard positional numeral systems

The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation.

Non-standard positional numeral systems

Bijective numeration

Signed-digit representation

Negative bases A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is ...

The common names of the negative base numeral systems are formed using the prefix ''nega-'', giving names such as:

Complex bases

Non-integer bases

''n''-adic number

Mixed radix

* Factorial number system * Even double factorial number system * Odd double factorial number system * Primorial number system *

Fibonorial In mathematics, the Fibonorial , also called the Fibonacci factorial, where is a nonnegative integer, is defined as the product of the first positive Fibonacci numbers, i.e. : _F := \prod_^n F_i,\quad n \ge 0, where is the th Fibonacci number, ...

number system * in timekeeping * in timekeeping * (12, 20) traditional English monetary system (£sd) * (20, 18, 13) Maya timekeeping

Other

* Quote notation *

Redundant binary representation A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary Numerical digit, digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, includi ...

* Hereditary base-n notation * Asymmetric numeral systems optimized for non-uniform probability distribution of symbols * Combinatorial number system

Non-positional notation

All known numeral systems developed before the Babylonian numerals are non-positional,Chrisomalis calls the Babylonian system "the first positional system ever" in . as are many developed later, such as the

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

. The French Cistercian monks created their own numeral system.

References

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Systems A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...