Mixed radix

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (July 2021) (Learn how and when to remove this message)

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:

... 32, 5, 07, 45; 15,  500
...  ∞, 7, 24, 60; 60, 1000

or as

32_∞5₇07₂₄45₆₀.15₆₀500₁₀₀₀

In the tabular format, the digits are written above their base, and a semicolon indicates the radix point. In numeral format, each digit has its associated base attached as a subscript, and the radix point is marked by a full stop or period. 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 one could not add a larger unit of "month" or "year" to the sequence of units, as they are not integer multiples of "week").