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.
See also
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Table of bases
This table of bases gives the values of 0 to 256 in bases 2 to 36, using A−Z for 10−35.
"Base" (or "radix") is a term used in discussions of numeral systems which use place-value notation for representing numbers.
Base 10 is in bold.
...
– 0 to 74 in base 2 to 36
*
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 express ...