Hamming and Extended Parity Code Calculator
Encode four data bits or inspect a seven/eight-bit Hamming codeword under explicit error-count assumptions.
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
Place data at positions 3,5,6,7 and even parity at 1,2,4. Extended mode adds overall parity at position 8 and uses syndrome plus overall parity to distinguish supported cases.
Syndrome=sum(parity-check position weights that fail); extended overall parity distinguishes supported single/double errors
Worked example
Data 1011 encodes as Hamming 0110011 and extended 01100110 with positions read left to right from 1.
Assumptions and input details
Seven-bit mode assumes at most one error and cannot reliably detect double errors. Extended mode handles at most one error for correction and two for detection; higher error counts can mimic other cases. Detected double-error cases do not receive a claimed corrected data word. No packet transmission or file access.
References: Carnegie Mellon: Hamming parity-check structure
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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