List of numeral systems

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

By culture / time period
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base).

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.

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.