Description
Generate an exact unsigned integer with a specified positive bit length, setting the top bit and drawing remaining bits independently; integer text avoids unsafe numbers.
A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.
Generate an exact unsigned integer with a specified positive bit length, setting the top bit and drawing remaining bits independently; integer text avoids unsafe numbers.
When to use this tool
Use this tool to generate an exact unsigned integer with a specified positive bit length, setting the top bit and drawing remaining bits independently; integer text avoids unsafe numbers.
How to use the tool and how it works
- Enter bits, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.value, result.binary, using the stated boundary, ordering, sign and absence conventions.
Require bits in 1–128. Set the leading bit to one, then append bits−1 independent binary draws. Return exact decimal value and its binary spelling.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| bits | Exact positive integer bit length, 1–128, with a forced leading one. | Finite safe integer satisfying the stated bounds. |
| seed | Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.seed | Original supplied seed string; injected-source replay additionally requires that source’s state. |
| result.value | Selected literal member or exact integer text, under the stated generator. |
| result.binary | Exact binary spelling with the requested bit length. |
{
"input": {
"bits": 4,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"value": "15",
"binary": "1111"
}
}
}Limitations and assumptions
- Support is positive integers of exactly the stated bit length, not all integers from zero through 2^bits−1.
- A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.
Alternative or Complementary methods
Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.
References
Similar or alternative tools
- Random Contiguous Bit Burst Mask
Choose one uniform nonwrapping contiguous positive bit burst start; the mask is left-to-right text, not an encoded integer.
- Random Reflecting Integer Walk
Generate fair independent unit-step proposals and reflect outward steps inward at either endpoint in an explicit bounded integer interval; every step consumes a proposal, including steps taken from a boundary.