Description
Apply one end-around-carry addition step.
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.
Apply one end-around-carry addition step.
When to use this tool
Use Ones Complement End Around Carry Step when checking the stated fixed-width representation or encoding convention.
How to use the tool and how it works
- Enter sum, width. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read word, carry. Inspect carry before interpreting the associated values.
Apply one end-around-carry addition step. Require width 1..128 and exact nonnegative sum <= twice the all-ones mask; carry means sum exceeds mask, word = low width bits plus that carry.1
One's-complement checksum arithmetic uses end-around carry and has two zero encodings. A single word operation is only part of a complete message checksum.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sum | Sum | 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 128. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| word | Word | Required. Text; maximum UTF-16 length 8192. |
| carry | One end-around carry from adding two bounded words; not a whole-message checksum result. | Required. Boolean. |
{
"input": {
"sum": "258",
"width": 8
},
"output": {
"word": "3",
"carry": true
}
}Limitations and assumptions
- This is one one's-complement addition step, not a complete checksum, complemented output or network-byte-order parser.
- 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
-
Calculation and input contract: bitwise/ones-complement-end-around-carry-step — tool.io
-
Computing the Internet Checksum, RFC 1071 — Internet Engineering Task Force
Similar or alternative tools
- Ones Complement Dual Zero Equality
Compare one's-complement words with dual-zero equality.
- Ones Complement Checksum Zero Canonicalizer
Canonicalize either one's-complement zero pattern.