Fixed Point Range Envelope
Report the exact representable rational envelope of a signed or unsigned binary fixed-point word; no floating approximation.
Description
Report the exact representable rational envelope of a signed or unsigned binary fixed-point word; no floating approximation.
A fixed-point range combines an integer field envelope with the scale 2^fractionalBits.
When to use this tool
Report the exact representable rational envelope of a signed or unsigned binary fixed-point word; no floating approximation.
- Prepare the supplied bits, fractionalBits, signed 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, fractionalBits, signed. 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.minimum, result.maximum. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
For bits 1 to 128 and fractionalBits 0 to 128, form signed or unsigned minimum and maximum integer numerators and attach denominator 2^fractionalBits to both.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| bits | bits. | Integer from 1 to 128 inclusive |
| fractionalBits | fractional bits. | Integer from 0 to 128 inclusive |
| signed | Explicit choice for signed; supply a boolean rather than a text label. | true or false |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.minimum | The minimum value under the stated formula or text convention. |
| result.maximum | The maximum value under the stated formula or text convention. |
{
"input": {
"bits": 4,
"fractionalBits": 2,
"signed": true
},
"output": {
"result": {
"minimum": {
"numerator": "-8",
"denominator": "4"
},
"maximum": {
"numerator": "7",
"denominator": "4"
}
}
}
}Limitations and assumptions
- The displayed fractions are not necessarily reduced. fractionalBits is independent of total bits, and no floating-point exponent model or rounding is included.
- Exact decimal-spelling operations require digits before the optional decimal point and allow a signed exponent. Decimal text is bounded to 256 code units and effective scale to minus 256 through 256; integer-string fields allow a sign and up to 256 digits.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Preserve decimal and integer strings when exact comparisons matter. Select signedness, scale, rounding and overflow policies separately, and use the matching encoder/decoder rather than a floating-point approximation.
References
Similar or alternative tools
- Fixed Point Add Overflow Flag
Add exact raw fixed-point integers and flag explicit signed or unsigned word overflow; does not wrap or saturate.
- Fixed Point Division and Rescale
Exact raw fixed-point division and rescaling, truncating toward zero while retaining signed remainder evidence.