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 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.
A standard form for dates is 2021-04-10 16:31:15, which would be a mixed radix number by this definition, with the consideration that the quantities of days vary both per month, and with leap years.
In addition, a long count of vigesimal days, octodecimal winal, then base 24 tun, k'atun, b'ak'tun, etc., tracks historical dates.
A second example of a mixed-radix numeral system in current use is in the design and use of currency, where a limited set of denominations are printed or minted with the objective of being able to represent any monetary quantity; the amount of money is then represented by the number of coins or banknotes of each denomination.
− 1 and permutations of n elements in lexicographic order, which uses the factorial representation of the integer, followed by an interpretation as a Lehmer code.