Binary Polynomial CRC Calculator
Encode a raw binary message or check a received codeword by explicit generator-polynomial division.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
For encoding append degree-many zero bits before modulo-two division. XOR the generator where each leading dividend bit is one; the final degree-many bits are the remainder.
Codeword=message followed by remainder of message×x^degree divided by generator over GF(2)
Worked example
Message 11010011101100 with generator 1011 has remainder 100. The appended codeword 11010011101100100 divides with zero remainder.
Assumptions and input details
Raw polynomial arithmetic with 1–8192 message bits and generator degree 1–32. No reflected-bit order, nonzero initial register or final XOR; this is not a claim to implement a named CRC-32 protocol. A zero remainder means divisible by this generator, not proof of error-free data or authentication.
References: Williams College: CRC polynomial division
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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