Description
Negate a word modulo its width and flag signed minimum overflow.
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.
Negate a word modulo its width and flag signed minimum overflow.
When to use this tool
Use Bitwise: Twos Complement Minimum Negation Check 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 result. Expand result to inspect the returned fields.
Negate a word modulo its width and flag signed minimum overflow. Validate bounded word; negatedWord = (2^width-word) modulo 2^width, overflow means word === 2^(width-1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| word | Word | Required. Text. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. Word value must satisfy 0 <= value < 2^width. |
| width | Width under the stated bit, interval or geometry convention; apply the field-specific units and bounds. | Required. Safe integer. Fixed-word implementation domain: whole width 1-128 bits. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.negatedWord | Negated Word | Calculated result member: string. |
| result.overflow | True for the most-negative signed input even though its fixed-width absolute bit pattern is unchanged. | Calculated result member: boolean. |
{
"input": {
"word": "128",
"width": 8
},
"output": {
"result": {
"negatedWord": "128",
"overflow": true
}
}
}Limitations and assumptions
- Zero negates to itself without overflow; the flag uses two's-complement signed interpretation rather than unsigned underflow.
- Outputs are nested inside result. 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 Negation Fixed Point
Check fixed points of modular signed negation.
- Bitwise: Ones Complement Negative Zero Check
Check one's-complement negative zero.