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The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base.In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten.
The most familiar example of mixed-radix systems is in timekeeping and calendars. Western time radices include, both cardinally and ordinally, decimal years, decades, and centuries, septenary for days in a week, duodecimal months in a year, bases 28–31 for days within a month, as well as base 52 for weeks in a year.
The smallest base greater than binary such that no three-digit narcissistic number exists. 80: Octogesimal: Used as a sub-base in Supyire. 85: Ascii85 encoding. This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 ...
The standard 12-hour clock and common use of 12 in English units emphasize the utility of the base. In addition, prior to its conversion to decimal, the old British currency Pound Sterling (GBP) partially used base-12; there were 12 pence (d) in a shilling (s), 20 shillings in a pound (£), and therefore 240 pence in a pound.
The single-trit addition, subtraction, multiplication and division tables are shown below. For subtraction and division, which are not commutative, the first operand is given to the left of the table, while the second is given at the top. For instance, the answer to 1 − T = 1T is found in the bottom left corner of the subtraction table.
Another use of the base is to show the silver ratio as its representation in base √ 2 is simply 11 √ 2. In addition, the area of a regular octagon with side length 1 √ 2 is 1100 √ 2, the area of a regular octagon with side length 10 √ 2 is 110000 √ 2, the area of a regular octagon with side length 100 √ 2 is 11000000 √ 2, etc…
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