Arranged by base

• Radix
  Radix
  In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...
  
  , radix point
  Radix point
  In mathematics and computing, a radix point is the symbol used in numerical representations to separate the integer part of a number from its fractional part . "Radix point" is a general term that applies to all number bases...
  
  , mixed radix
  Mixed radix
  Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same...
  
  , base (mathematics)
• Unary numeral system
  Unary numeral system
  The unary numeral system is the bijective base-1 numeral system. It is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol representing 1 is repeated N times. For example, using the symbol | , the number 6 is represented as ||||||...
  
   (base 1)
  • Tally marks
    Tally marks
    Tally marks, or hash marks, are a unary numeral system. They are a form of numeral used for counting. They allow updating written intermediate results without erasing or discarding anything written down...
    
    
• Binary numeral system
  Binary numeral system
  The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
  
   (base 2)
• Negative base
  Negative base
  A negative base 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 to say, the base \scriptstyle b is equal to \scriptstyle -r for some...
  
   numeral system (base −2)
• Ternary numeral system
  Ternary numeral system
  Ternary is the base- numeral system. Analogous to a bit, a ternary digit is a trit . One trit contains \log_2 3 bits of information...
  
   numeral system (base 3)
• Balanced ternary
  Balanced ternary
  Balanced ternary is a non-standard positional numeral system , useful for comparison logic. It is a ternary system, but unlike the standard ternary system, the digits have the values −1, 0, and 1...
  
   numeral system (base 3)
• Negative base
  Negative base
  A negative base 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 to say, the base \scriptstyle b is equal to \scriptstyle -r for some...
  
   numeral system (base −3)
• Quaternary numeral system
  Quaternary numeral system
  Quaternary is the base- numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation and the characteristics of the representations of...
  
   (base 4)
• Quater-imaginary base
  Quater-imaginary base
  The quater-imaginary numeral system was first proposed by Donald Knuth in 1955, in a submission to a high-school science talent search. It is a non-standard positional numeral system which uses the imaginary number 2i as its base. It is able to uniquely represent every complex number using only...
  
   (base 2√−1)
• Quinary
  Quinary
  Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. The base five is stated from 0-4...
  
   numeral system (base 5)
  • Pentimal system
    Pentimal system
    The pentimal system is a notation for presenting numbers, usually by inscribing in wood or stone. The notation has been used in Scandinavia, usually in conjunction to runes....
    
    
• Senary
  Senary
  In mathematics, a senary numeral system is a base- numeral system.Senary may be considered useful in the study of prime numbers since all primes other than 2 and 3, when expressed in base-six, have 1 or 5 as the final digit...
  
   numeral system (base 6)
• Septenary
  Septenary
  The septenary numeral system is the base- number system, and uses the digits 0-6.-Multiplication table:-Fractions:Fractions expressed in septenary will repeat a sequence of digits unless the denominator is a power of seven...
  
   numeral system (base 7)
• Octal
  Octal
  The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...
  
   numeral system (base 8)
• Nonary
  Nonary
  Nonary is a base- numeral system, typically using the digits 0-8, but not the digit 9.The first few numbers in nonary and decimal are:Nonary 1 2 3 4 5 6 7 81011121314Decimal 1 2 3 4 5 6 7 8 910111213The...
  
   (novenary) numeral system (base 9)
• Decimal
  Decimal
  The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
  
   (denary) numeral system (base 10)
  • Bi-quinary coded decimal
    Bi-quinary coded decimal
    Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, including the Colossus. The term bi-quinary indicates that the code comprises both a two-state and a five-state component...
    
    
• Negative base
  Negative base
  A negative base 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 to say, the base \scriptstyle b is equal to \scriptstyle -r for some...
  
   numeral system (base −10)
• Duodecimal
  Duodecimal
  The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...
  
   (dozenal) numeral system (base 12)
• Hexadecimal
  Hexadecimal
  In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
  
   numeral system (base 16)
• Vigesimal
  Vigesimal
  The vigesimal or base 20 numeral system is based on twenty .- Places :...
  
   numeral system (base 20)
• Sexagesimal numeral system (base 60)

Arranged by culture

• Australian Aboriginal enumeration
  Australian Aboriginal enumeration
  A common misconception among non-Aboriginals is that Aboriginals did not have a way to count beyond two or three. However, Alfred Howitt, who studied the peoples of southeastern Australia, disproved this in the late nineteenth century, although the myth continues in circulation today.The...
  
  
• Armenian numerals
  Armenian numerals
  The system of Armenian numerals is a historic numeral system created using the majuscules of the Armenian alphabet.There was no notation for zero in the old system, and the numeric values for individual letters were added together. The principles behind this system are the same as for the Ancient...
  
  
• Babylonian numerals
  Babylonian numerals
  Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record....
  
  
• Chinese numerals
  Chinese numerals
  Chinese numerals are characters for writing numbers in Chinese. Today speakers of Chinese use three numeral systems:the ubiquitous Arabic numerals and two indigenous systems....
  
  
  • Counting rods
    Counting rods
    Counting rods are small bars, typically 3–14 cm long, used by mathematicians for calculation in China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any number and any fraction....
    
    
• Aegean numbers
• Greek numerals
  Greek numerals
  Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...
  
  
• Hebrew numerals
  Hebrew numerals
  The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet.In this system, there is no notation for zero, and the numeric values for individual letters are added together...
  
  
• Hindu–Arabic numeral system
  • Arabic numerals
    Arabic numerals
    Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
    
    
  • Indian numerals
    Indian numerals
    Most of the positional base 10 numeral systems in the world have originated from India, where the concept of positional numeration was first developed...
    
    
  • Thai numerals
    Thai numerals
    Thai numerals constitute a numeral system of Thai number names for the Khmer numerals traditionally used in Thailand, also used for the more common Arabic numerals, and which follow the Hindu-Arabic numeral system.-Usage:...
    
    
• Japanese numerals
  Japanese numerals
  The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000...
  
  
• Korean numerals
  Korean numerals
  The Korean language has two regularly used sets of numerals, a native Korean system and Sino-Korean system.-Construction:For both native and Sino- Korean numerals, the teens are represented by a combination of tens and the ones places...
  
  
• Maya numerals
  Maya numerals
  Maya Numerals were a vigesimal numeral system used by the Pre-Columbian Maya civilization.The numerals are made up of three symbols; zero , one and five...
  
  
• Moksha numerals
• Prehistoric numerals
• Roman numerals
  Roman numerals
  The numeral system of ancient Rome, or Roman numerals, uses combinations of letters from the Latin alphabet to signify values. The numbers 1 to 10 can be expressed in Roman numerals as:...
  
  
• Welsh numerals
  Welsh numerals
  The traditional counting system used in the Welsh language is vigesimal, i.e. based on twenties, as in the French numerals for 60-99, where numbers from 11–14 are "x on ten", 16–19 are "x on fifteen" ; numbers from 21–39 are "1–19 on twenty", 40 is "two twenty", 60 is "three twenty", etc.There is...
  
  

Other

• Algorism
  Algorism
  Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist...
  
  
• Goodstein's theorem
  Goodstein's theorem
  In mathematical logic, Goodstein's theorem is a statement about the natural numbers, made by Reuben Goodstein, which states that every Goodstein sequence eventually terminates at 0. showed that it is unprovable in Peano arithmetic...
  
  
• Myriad
  Myriad
  Myriad , "numberlesscountless, infinite", is a classical Greek word for the number 10,000. In modern English, the word refers to an unspecified large quantity.-History and usage:...
  
  
• Non-standard positional numeral systems
  Non-standard positional numeral systems
  Non-standard positional numeral systems here designates numeral systems that may be denoted positional systems, but that deviate in one way or another from the following description of standard positional systems:...
  
  
• Quipu
  Quipu
  Quipus or khipus were recording devices used in the Inca Empire and its predecessor societies in the Andean region. A quipu usually consisted of colored, spun, and plied thread or strings from llama or alpaca hair. It could also be made of cotton cords...
  
  
• Long and short scales
  Long and short scales
  The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...
  
  
• Tally stick
  Tally stick
  A tally was an ancient memory aid device to record and document numbers, quantities, or even messages. Tally sticks first appear as notches carved on animal bones, in the Upper Paleolithic. A notable example is the Ishango Bone...
  
  
• Tally mark
• -yllion
  -yllion
  -yllion is a proposal from Donald Knuth for the terminology and symbols of an alternate decimal superbase system. In it, he adapts the familiar English terms for large numbers to provide a systematic set of names for much larger numbers...