List of numeral systems

"See also: List of types of numbers" There are many different numeral systems, that is, writing systems for expressing numbers.

By type of notation
Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix 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.

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

Mixed radix

 * Factorial number system {1, 2, 3, 4, 5, 6, ...}
 * Even double factorial number system {2, 4, 6, 8, 10, 12, ...}
 * Odd double factorial number system {1, 3, 5, 7, 9, 11, ...}
 * Primorial number system {2, 3, 5, 7, 11, 13, ...}
 * Fibonorial number system {1, 2, 3, 5, 8, 13, ...}
 * {60, 60, 24, 7} in timekeeping
 * {60, 60, 24, 30 (or 31 or 28 or 29), 12, 10, 10, 10} 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, as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.