Description
Check fixed points of modular signed negation.
A fixed-width bit pattern and the number it represents are different concepts. Unsigned, two's-complement, one's-complement, sign-magnitude and biased encodings use different sign and zero conventions, so a bit-preserving transformation need not preserve numerical meaning.
Check fixed points of modular signed negation.
When to use this tool
Use Signed Word Negation Fixed Point when checking the stated fixed-width representation or encoding convention.
How to use the tool and how it works
- Enter word, width. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fixedPoint, signedDecimal. Inspect fixedPoint before interpreting the associated values.
Check fixed points of modular signed negation. Require width 1..256 and bounded decimal word; fixedPoint means (2^width-word) modulo 2^width equals word, signedDecimal applies two's-complement interpretation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| word | Word | Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. |
| width | Width under the stated bit, interval or geometry convention; apply the field-specific units and bounds. | Required. Safe integer; minimum 1; maximum 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fixedPoint | Fixed Point | Required. Boolean. |
| signedDecimal | Signed Decimal | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"word": "128",
"width": 8
},
"output": {
"fixedPoint": true,
"signedDecimal": "-128"
}
}Limitations and assumptions
- Both zero and the signed-minimum bit pattern are fixed points; the latter is not zero and overflows ordinary signed negation.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Choose an explicit representation and width, validate the complete encoded value and use the matching signed or unsigned conversion for the intended numerical interpretation.
References
Similar or alternative tools
- Signed Word Sign Extension Gap
Sign-extend a word from source width to target width.
- Signed Magnitude Add Sign Conflict
Compare signed-magnitude operands for opposing nonzero signs.