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One's Complement Bit Pattern Calculator — result sheet
Invert a fixed-width binary word and interpret the result using one's-complement signed arithmetic, including the negative-zero case.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Within a w-bit word, complement(x) = (2ʷ−1) XOR x. If the complemented word's top bit is 0 its signed value is positive; if it is 1, invert the word again and negate that magnitude, with all-zero magnitude representing negative zero.
One's complement represents a signed word by keeping positive values ordinary and representing a negative value as the bitwise inversion of its positive magnitude. The fixed width matters: the same decimal value has a different complement in four bits than in eight bits. This page first treats the entered number as an unsigned bit pattern, inverts exactly the selected number of bits, and then reports both the raw result and its signed one's-complement interpretation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Unsigned bit-pattern value — Enter a decimal whole number that fits the selected width.
- Word width — 4 choices
Worked example
| Input | Value |
|---|---|
| Unsigned bit-pattern value | 5 |
| Word width | 8 |
00000101 complements to 11111010; the unsigned pattern is 250 and its one's-complement signed interpretation is −5.
Assumptions and limits
- The entered value is a nonnegative decimal integer used as an unsigned bit pattern.
- The selected width is exactly 4, 8, 16, or 32 bits and the value must fit that width.
- The complement is performed only inside the selected word; bits above the width do not participate.
- Signed interpretation follows one's-complement rules and therefore has both positive zero and negative zero.
- This page does not model two's-complement overflow, machine-language casts, or a CPU's signed-integer type.
- Bit strings are displayed most-significant bit first with leading zeroes preserved.
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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