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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]
For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores). The number the numeral represents is called its value.
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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"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
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