Talk:Mixed radix

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Here are some subtopics that might help the exposition along once the proper references are dug up …

Contents 1 Why each radix must be an integer 2 1 is a perfectly good radix 3 Proper and improper MRNs 4 Carry 5 Addition and scalar multiplication 6 Conversion between MRN systems

[edit] Why each radix must be an integer

For example Dollars/Quarters/Nickels/Pennies makes a perfectly good MRN system, but Dollars/Quarters/Dimes/Nickels/Pennies doesn't because the radix Dimes -> Quarters is 2.5, and 0₁₀0₄2_2.50₂4₅ (2-dimes,4-pennies) doesn't know whether to roll over to 0₁₀0₄2_2.51₂0₅ (2-dimes,1-nickel) or 0₁₀1₄0_2.50₂0₅ (1-quarter).

[edit] 1 is a perfectly good radix

Radix 1 digits can act as place holders, but don't otherwise affect the MRN system.

[edit] Proper and improper MRNs

"Improper" MRNs have digits equal to or greater than their radices. They still specify integers, but these may not be limited to the product of the radices minus 1.

[edit] Carry

Procedure to generate the proper MRN from an improper one if the integer represented is within range. Uses truncating division and the modulo operator. Overflow results if the integer is not in range.

[edit] Addition and scalar multiplication

Addition defined in the obvious way on two MRNs with the same base produces in general an improper MRN, which is rendered into a proper one using carry (with the possibility of overflow). Scalar multiplication on an MRN is just multiplying all the digits by a (non-negative) integer. Again carry is applied and overflow is a possibility.

[edit] Conversion between MRN systems

Obvious algorithms for doing this using the above tools are well known (so says I, research to be done :-) Doing these conversions efficiently seems to be a serious issue in Computer Science.

--J. W. McLeod 19:04, 27 Mar 2005 (UTC)