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:The most familiar example of mixed radix systems is in timekeeping and calendars. Western time radices include decimal centuries, decades and years as well as duodecimal months, trigesimal (and untrigesimal and (for February) octovigesimal and enneavigesimal) days, overlapped with duoquinquagesimal weeks and septenary days. One variant uses tridecimal months, quaternary weeks, and septenary days. Time is further divided by quadrivigesimal hours, sexagesimal minutes and seconds, then decimal fractions thereof.Mixed-radix numbers of the same base can be manipulated using a generalization of manual arithmetic algorithms. Conversion of values from one mixed base to another is easily accomplished by first converting the place values of the one system into the other, and then applying the digits from the one system against these.Another proposal is the so-called factorial number system:Another proposal is the number system with successive prime numbers as radix, whose place values are primorial numbers: