duodecimalˌdu əˈdɛs ə məl, ˌdyu-
duodecimal (n)
English Definitions:
one-twelfth, twelfth, twelfth part, duodecimal (adj)
one part in twelve equal parts
duodecimal (adj)
based on twelve
"the duodecimal number system"
duodecimal (Noun)
A number system that uses 12 as its base.
duodecimal (Adjective)
Of a number, expressed in 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". The number twelve is instead written as "10" in duodecimal, whereas the digit string "12" means "1 dozen and 2 units". Similarly, in duodecimal "100" means "1 gross", "1000" means "1 great gross", and "0.1" means "1 twelfth". The number twelve, a highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers, duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. As a result, duodecimal is sometimes considered the most optimal number system. Of its factors, 2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a terminating representation in duodecimal. In particular, the five most elementary fractions all have a short terminating representation in duodecimal, and twelve is the smallest radix with this feature. This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary, octal and hexadecimal systems, although the sexagesimal system does better in this respect.
Duodecimal
The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead written as "10" in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (decimal 14). Similarly, in duodecimal, "100" means "1 gross", "1000" means "1 great gross", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth", respectively). Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses A and B, as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: ↊ (a turned 2) for ten and ↋ (a turned 3) for eleven. The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range, and the smallest abundant number. All multiples of reciprocals of 3-smooth numbers (a/2b·3c where a,b,c are integers) have a terminating representation in duodecimal. In particular, +1⁄4 (0.3), +1⁄3 (0.4), +1⁄2 (0.6), +2⁄3 (0.8), and +3⁄4 (0.9) all have a short terminating representation in duodecimal. There is also higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system.In these respects, duodecimal is considered superior to decimal (which has only 2 and 5 as factors) and other proposed bases like octal or hexadecimal. Sexagesimal does even better in this respect (the reciprocals of all 5-smooth numbers terminate), but at the cost of unwieldy multiplication tables and a much larger number of symbols to memorize.
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"duodecimal." Kamus.net. STANDS4 LLC, 2024. Web. 20 Apr. 2024. <https://www.kamus.net/english/duodecimal>.
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