Bit String Rank One Query

Count 1 bits in the half-open prefix before an explicit endpoint; rank excludes the endpoint position itself.

Description

Count 1 bits in the half-open prefix before an explicit endpoint; rank excludes the endpoint position itself.

A rank-one query counts set positions in a half-open prefix of a bitstring.

When to use this tool

Count 1 bits in the half-open prefix before an explicit endpoint; rank excludes the endpoint position itself.

Prepare the supplied bits, end 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 bits, end. 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.

Require end from zero through string length and count ones in the slice [0, end).^[1]

Input field	Meaning and representation	Accepted input
bits	bits.	Binary text containing only 0 and 1; at most 128 characters
end	end.	Integer from 0 to bits.length inclusive

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

json

{
  "input": {
    "bits": "10100",
    "end": 4
  },
  "output": {
    "result": {
      "rank": 2
    }
  }
}

Limitations and assumptions

The boundary is exclusive and positions are left-to-right text indexes. No packed integer representation is inferred.
Every bitstring is at most 128 characters and contains only literal zero and one.
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

Choose a packed-integer or textual-bit representation deliberately before combining operations. Preserve the documented index direction, width and exclusive boundaries; do not substitute a rank query for select.

References

Tool behavior and example: Bit String Rank One Query — tool.io

Similar or alternative tools

Bit String Rank Zero Query
Count 0 bits in the half-open prefix before an explicit endpoint; rank excludes the endpoint position itself.
Bit String Select One Query
Select a zero-based occurrence of bit 1 in an explicit bit string; null denotes an occurrence beyond the observed count.