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Two’s Complement Converter — result sheet
Encode a signed integer into a fixed-width two’s-complement bit pattern and decode the same pattern back to its signed and unsigned values.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For width w, encode n as n mod 2^w and write that unsigned residue in exactly w binary bits; decode values with a leading 1 as residue − 2^w.
Two’s complement assigns the most significant bit a negative weight while keeping ordinary binary addition useful. The converter enforces the signed range for the selected width and reports the fixed-width pattern, unsigned residue, and decoded signed value.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Signed integer — minimum -2147483648; maximum 2147483647
- Bit width — 4 choices
Worked example
| Input | Value |
|---|---|
| Signed integer | -37 |
| Bit width | 8 |
−37 in 8-bit two’s complement is 11011011; its unsigned residue is 219, which decodes back to −37.
Assumptions and limits
- The input is an integer represented in a fixed width of 4, 8, 16, or 32 bits.
- Overflow is rejected rather than silently wrapping to a different signed value.
- The bit pattern is interpreted as two’s complement, not sign-magnitude or one’s complement.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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