There are many different

numeral system A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbo ...

s, that is,

writing system A writing system is a method of visually representing verbal communication, based on a script and a set of rules regulating its use. While both writing and speech are useful in conveying messages, writing differs in also being a reliable fo ...

s 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 th ...

(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 ...

or base.

Standard positional numeral systems

The common names are derived somewhat arbitrarily from a mix of

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

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 In mathematical notation for numbers, a signed-digit representation is a positional numeral system with a set of signed digits used to encode the integers. Signed-digit representation can be used to accomplish fast addition of integers be ...

Negative bases

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

Other

* Quote notation * Redundant binary representation * 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, ...

. The French Cistercian monks created their own numeral system.

References

{{Reflist

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 expresse ...