# Mixed radix

**Mixed radix** numeral systems are unique in that the numerical base may vary from position to position. Such numerical representation is advantageous when representing units that are equivalent to each other, but not by the same ratio. For example, 2 weeks, 5 days, 7 hours, 45 minutes, 15 seconds, and 500 milliseconds can be rendered in mixed-radix notation as:

The digits are written above their base, and a semicolon is used to indicate the radix point.

Mixed-radix numbers of the same base can be manipulated using a generalization of manual arithmetic algorithms.

Donald E. Knuth.

*The Art of Computer Programming*, Volume 2. pp209