Mixed Radix Digit Encoder

Encode bounded mixed-radix digits most-significant lane first into exact integer text; every radix is positive and every digit must fit.

Description

Encode bounded mixed-radix digits most-significant lane first into exact integer text; every radix is positive and every digit must fit.

Mixed-radix encoding maps one valid digit vector to a zero-based exact integer index.

When to use this tool

Encode bounded mixed-radix digits most-significant lane first into exact integer text; every radix is positive and every digit must fit.

Prepare the supplied digits, radices fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter digits, radices. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.index. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Require equal list lengths, each radix from 1 to one million and each digit from zero through radix minus one. Fold index = index*radix plus digit from left to right and return decimal text.^[1]

Input field	Meaning and representation	Accepted input
digits	digits.	List of finite numbers; at most 128 entries
radices	radices.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.index	The index value under the stated formula or text convention.

json

{
  "input": {
    "digits": [
      1,
      2
    ],
    "radices": [
      2,
      3
    ]
  },
  "output": {
    "result": {
      "index": "5"
    }
  }
}

Limitations and assumptions

The last digit is least significant. Empty lists encode as zero, without defining any external coordinate layout.
All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.

Alternative or Complementary methods

Retain the universe size, subset size and ordering convention with a rank. Use rank/unrank pairs from the same convention and distinguish subset masks from lexicographic indexes.

References

Tool behavior and example: Mixed Radix Digit Encoder — tool.io

Similar or alternative tools

Mixed Radix Digit Decoder
Decode a zero-based exact integer index into mixed-radix digits most-significant lane first; out-of-range indexes do not wrap.
Mixed Radix Next Digits
Advance a mixed-radix tuple forward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.