Mixed Radix

Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same factor. Such units are common for instance in measuring time; a time of 32 weeks, 5 days, 7 hours, 45 minutes, 15 seconds, and 500 milliseconds might be expressed as a number of minutes in mixed-radix notation as:

or as

32_∞5₇7₂₄45₆₀.15₆₀500₁₀₀₀

In the tabular format, the digits are written above their base, and a semicolon is used to indicate the radix point. In numeral format, each digit has its associated base attached as a subscript, and the position of the radix point is indicated by a full stop. The base for each digit is the number of corresponding units that make up the next larger unit. As a consequence there is no base (written as ∞) for the first (most significant) digit, since here the "next larger unit" does not exist (and note that one could not add a larger unit of "month" or "year" to the sequence of units, as they are not integer multiples of "week").