Bitwise: Word Signedness Reinterpretation Tool

Description

Reinterpret a bounded word as unsigned and two's-complement signed integers.

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.

Reinterpret a bounded word as unsigned and two's-complement signed integers.

When to use this tool

Use Bitwise: Word Signedness Reinterpretation 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.

Reinterpret a bounded word as unsigned and two's-complement signed integers. Validate decimal word within its width; unsigned preserves its value, signed subtracts 2^width when the highest bit is set; return exact decimal strings.^[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	Fixed word width 1..128 bits under this helper's implementation domain.	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.unsigned	Unsigned	Calculated result member: string.
result.twosComplementSigned	Twos Complement Signed	Calculated result member: string.

json

{
  "input": {
    "word": "255",
    "width": 8
  },
  "output": {
    "result": {
      "unsigned": "255",
      "twosComplementSigned": "-1"
    }
  }
}

Limitations and assumptions

The bit pattern is retained rather than numerically converted between encodings; no byte order or memory representation is inferred.
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

Calculation and input contract: bitwise/word-signedness-reinterpretation — tool.io

Similar or alternative tools

Signed Word Sign Extension Gap
Sign-extend a word from source width to target width.
Bitwise: Sign Magnitude Word To Integer
Decode a sign-magnitude word with negative-zero policy.