Fixed Weight Binary Word Rank
Rank a fixed-weight binary word lexicographically by its zero-position combination, using exact zero-based integer text.
Description
Rank a fixed-weight binary word lexicographically by its zero-position combination, using exact zero-based integer text.
Fixed-weight binary words can be ranked without listing every word. This convention follows lexicographic order of the zero-position combination.
When to use this tool
Rank a fixed-weight binary word lexicographically by its zero-position combination, using exact zero-based integer text.
- Prepare the supplied word 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 word. 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.rank. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate word as a binary string, collect its zero indexes in increasing order and compute their zero-based combination rank among equally sized subsets of the word positions. Return rank as decimal text.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| word | word. | Binary text containing only 0 and 1; at most 128 characters |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.rank | The rank value under the stated formula or text convention. |
{
"input": {
"word": "0101"
},
"output": {
"result": {
"rank": "1"
}
}
}Limitations and assumptions
- The rank depends on the fixed length and zero count. This is not the word's ordinary binary integer value or colex rank.
- 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
Similar or alternative tools
- Next Fixed Weight Binary Word
Return the next lexicographic binary word with the same length and one-count, without wraparound; null marks the last fixed-weight word.
- Combination Colexicographic Rank
Exact zero-based colexicographic combination ranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.