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Mixed-radix representation is also relevant to mixed-radix versions of the Cooley–Tukey FFT algorithm, in which the indices of the input values are expanded in a mixed-radix representation, the indices of the output values are expanded in a corresponding mixed-radix representation with the order of the bases and digits reversed, and each ...
General mixed radix systems were studied by Georg Cantor. [2] The term "factorial number system" is used by Knuth, [3] while the French equivalent "numération factorielle" was first used in 1888. [4] The term "factoradic", which is a portmanteau of factorial and mixed radix, appears to be of more recent date. [5]
Radix, radix point, mixed radix, base (mathematics) Unary numeral system (base 1) Tally marks – Numeral form used for counting; Binary numeral system (base 2) Negative base numeral system (base −2) Ternary numeral system numeral system (base 3) Balanced ternary numeral system (base 3) Negative base numeral system (base −3)
The Natural Area Code, this is the smallest base such that all of 1 / 2 to 1 / 6 terminate, a number n is a regular number if and only if 1 / n terminates in base 30. 32: Duotrigesimal: Found in the Ngiti language. 33: Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong. 34
In contrast to decimal, or radix 10, which has a ones' place, tens' place, hundreds' place, and so on, radix b would have a ones' place, then a b 1 s' place, a b 2 s' place, etc. [2] For example, if b = 12, a string of digits such as 59A (where the letter "A" represents the value of ten) would represent the value 5 × 12 2 + 9 × 12 1 + 10 × ...
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For example, 100 in decimal has three digits, so its cost of representation is 10×3 = 30, while its binary representation has seven digits (1100100 2), so the analogous calculation gives 2×7 = 14. Likewise, in base 3 its representation has five digits (10201 3 ), for a value of 3×5 = 15, and in base 36 (2S 36 ) one finds 36×2 = 72.