Subset Bitmask Integer Decoder

Decode an exact bounded subset mask into ascending least-significant-bit indexes; masks with bits outside the explicit universe are rejected.

Description

Decode an exact bounded subset mask into ascending least-significant-bit indexes; masks with bits outside the explicit universe are rejected.

A subset bitmask uses bit j to indicate membership of index j. Decimal text preserves masks wider than a floating-point integer.

When to use this tool

Decode an exact bounded subset mask into ascending least-significant-bit indexes; masks with bits outside the explicit universe are rejected.

Prepare the supplied mask, size 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 mask, size. 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.indexes. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Require size from 0 to 128 and a nonnegative mask below 2^size. Return ascending indexes whose corresponding least-significant-bit-based mask bits are set.^[1]

Input field	Meaning and representation	Accepted input
mask	Exact decimal integer text; keep it quoted in JSON rather than converting through a floating-point number.	Optional leading + or - and 1 to 256 decimal digits; no whitespace
size	size.	Integer from 0 to 128 inclusive

Output field	Interpretation
result	Object containing the named outputs below.
result.indexes	The indexes list in the ordering and representation described above.

json

{
  "input": {
    "mask": "9",
    "size": 4
  },
  "output": {
    "result": {
      "indexes": [
        0,
        3
      ]
    }
  }
}

Limitations and assumptions

Index zero is the low bit, unlike left-to-right textual bitstrings. No values outside the declared universe are retained.
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: Subset Bitmask Integer Decoder — tool.io

Similar or alternative tools

Subset Bitmask Integer Encoder
Encode a bounded unique index subset into an exact nonnegative integer bitmask, with index zero as the least significant bit.
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.