Fraction Binary Grid Membership
Check exact rational membership on an explicitly chosen binary fixed-point grid, not merely denominator power-of-two termination.
Description
Check exact rational membership on an explicitly chosen binary fixed-point grid, not merely denominator power-of-two termination.
A binary fixed-point grid with b fractional bits consists of integer multiples of 2^-b. Membership can be checked exactly.
When to use this tool
Check exact rational membership on an explicitly chosen binary fixed-point grid, not merely denominator power-of-two termination.
- Prepare the supplied numerator, denominator, fractionalBits 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 numerator, denominator, fractionalBits. 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.member. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Normalize the fraction, require fractionalBits from 0 to 128 and test whether numerator times 2^fractionalBits is divisible by denominator.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| numerator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| denominator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| fractionalBits | fractional bits. | Integer from 0 to 128 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.member | Membership flag for the specific set and boundary convention above. |
{
"input": {
"numerator": "3",
"denominator": "8",
"fractionalBits": 2
},
"output": {
"result": {
"member": false
}
}
}Limitations and assumptions
- This checks grid spacing only. It does not impose a signed storage range, total word width or floating-point exponent limits.
- Numerator and denominator fields use exact decimal integer strings of at most 256 digits with an optional sign. Fractions are reduced with a positive denominator before the stated operation.
- 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
Use exact numerator/denominator operations when equality and boundary decisions matter. Convert to a decimal display only with an explicit rounding policy; a rounded display should not replace the exact result.
References
Similar or alternative tools
- Exact Fraction Addition
Exact rational addition using decimal integer text and coprime output; no IEEE-754 precision loss.
- Fraction Base Termination Check
Check exact rational termination in an explicit integer radix 2–36 by removing denominator factors shared with that radix.