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Encyclopedia > Base 24

As there are 24 hours in a day a numbering system based upon 24, and as the base 12 is convenient here some examples of the base 24 (quadrovigesimal) system. 24 (twenty-four) is the natural number following 23 and preceding 25. ... A duodecimal multiplication table The duodecimal (also known as base-twelve or dozenal) is a numeral system using twelve as its base. ...

Numeral systems

Arabic (Hindu)
Arabic (Abjad)
Attic (Greek)
D'ni (fictional)
Ionian (Greek)
Thai A numeral is a symbol or group of symbols that represents a number. ... Arabic numerals (also called Hindu numerals or Indian numerals ) are the most common set of symbols used to represent numbers. ... This page is a candidate for speedy deletion. ... Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodianus. ... The Babylonians used a base-60 (or sexagesimal) positional numeral system borrowed from the Sumerians. ... The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ... Myst franchise Games Myst Riven Myst III: Exile Myst IV: Revelation Myst V: End of Ages Uru: Ages Beyond Myst Ages of: Myst Riven Myst III: Exile Myst IV: Revelation Uru Novels Myst: The Book of Atrus   Tiana   Dni Comic Books #0   #1 Miscellaneous Dni Ages   The... The Etruscan numerals were used by the ancient Etruscans. ... The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. ... Ionian numerals were used by the ancient Greeks, possibly before the 7th century BC. They are also known by the names Milesian numerals or Alexandrian numerals. ... Khmer numerals are the numerals used in the Khmer language of Cambodia. ... The Pre-Columbian Maya civilization used a vigesimal (base-twenty) numeral system. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ... Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. ...

Unary (1)
Binary (2)
Ternary (3)
Senary (6)
Octal (8)
Decimal (10)
Duodecimal (12)
Base 13
Hexadecimal (16)
Vigesimal (20)
QuadroVigesimal (24)
Sexagesimal (60) The unary numeral system is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol is repeated N times. ... The binary numeral system represents numeric values using two symbols, typically 0 and 1. ... Ternary is the base-3 numeral system. ... A senary numeral system is a base-six numeral system. ... The octal numeral system is the base-8 number system, and uses the digits 0 to 7. ... Decimal, or less commonly, denary, usually refers to the base 10 numeral system. ... A duodecimal multiplication table The duodecimal (also known as base-twelve or dozenal) is a numeral system using twelve as its base. ... Base 13 is a nonstandard positional numeral system. ... In mathematics and computer science, hexadecimal, or simply hex, is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ... The vigesimal (base-twenty) is a numeral system which is based on twenty. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ...

 Decimal Equivalent 10 twentyfour 24 24 100 ? 24^2 = 576 1000 ? 24^3 = 13 824 10 000 ? 24^4 = 331 776 100 000 ? 24^5 = 7 972 624 1 000 000 ? 24^6 = 191 102 976 

Digits used for numerals ten-twentythree can be A..P (I and O skipped to prevent confusion with the digits 1 and 0).


Quadrovigesimal fractions are usually either very simple

 1/2 = 0.C 1/3 = 0.8 1/4 = 0.6 1/6 = 0.4 1/8 = 0.3 1/9 = 0.2G 1/C = 0.2 1/G = 0.1C 1/J = 0.18 

or complicated

 1/5 = 0.4K4K4K4K... recurring (easily rounded to 0.5 or 0.4K) 1/7 = 0.3A6LDH3A6... recurring 1/A = 0.29E9E9E9... recurring (rounded to 0.2A) 1/B = 0.248HAMKF6D248.. recurring (rounded to 0.24) 1/D = 0.1L795CN3GEJB1L7.. recurring (rounded to 0.1L) 1/P = 0.11111... recurring (rounded to 0.11) 1/11 = 0.0P0P0P... recurring (rounded to 0.0P) (1/(5*5)) 

As explained in recurring decimals, whenever a fraction is written in "decimal" notation, in any base, the fraction can be expressed exactly (terminates) if and only if all the prime factors of its denominator are also prime factors of the base. Thus, in base-10 (= 2×5) system, fractions whose denominators are made up solely of multiples of 2 and 5 terminate: ¹⁄8 = ¹⁄(2*2*2), ¹⁄20 = ¹⁄(2×2×5), and ¹⁄500 (22×53) can be expressed exactly as 0.125, 0.05, and 0.002 respectively. ¹⁄3 and ¹⁄7, however, recur (0.333... and 0.142857142857...). In the duodecimal (= 2×2×3) system, ¹⁄8 is exact; ¹⁄20 and ¹⁄500 recur because they include 5 as a factor; ¹⁄3 is exact; and ¹⁄7 recurs, just as it does in base 10. A recurring decimal is an expression representing a real number in the decimal numeral system, in which after some point the same sequence of digits repeats infinitely many times. ...

Arguably, factors of 3 are more commonly encountered in real-life division problems than factors of 5 (or would be, were it not for the decimal system having influenced our culture). Thus, in practical applications, the nuisance of recurring decimals is encountered less often when quadrovigesimal (or duodecimal) notation is used. A recurring decimal is an expression representing a real number in the decimal numeral system, in which after some point the same sequence of digits repeats infinitely many times. ...

However when recurring fractions do occur in quadrovigesimal notation, they sometimes have a very short period when it are numbers containing one o two factors of five as 52 = 25 is adjacent to 24. The other adjacent number, 23 is a prime number. So powers of five look funny in the quadrovigesimal notation :

 51 = 5 52 = 11 53 = 55 54 = 121 55 = 5A5 56 = 1331 57 = 5FF5 58 = 14641 

The multiples of decimal hundred are 44, 88, CC, GG, LL, 110, etc.

See also



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