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LFSR Checker

Validate and simulate Linear Feedback Shift Register (LFSR) sequences with polynomial coefficients and initial states.

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About This Tool

The LFSR Checker is a comprehensive online tool for analyzing Linear Feedback Shift Registers used in cryptography, digital signal processing, and error correction. Input your polynomial coefficients (in binary or hex), set the initial state, and specify the number of steps to generate the complete sequence. The tool validates your polynomial, simulates the LFSR operation step-by-step, displays the output sequence, and verifies maximal length properties. All calculations are performed client-side for instant results without server delays.
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How to Use

  1. Enter polynomial coefficients in binary (e.g.,
  2. or hexadecimal (e.g., 0xB).
  3. Set the initial state in the same format as the polynomial.
  4. Specify the number of steps to simulate (default
  5. .
  6. Choose output format: Binary, Hexadecimal, or Decimal.
  7. Click 'Generate Sequence' to run the LFSR simulation.
  8. View the generated sequence, state transitions, and polynomial verification results.
How to use lfsr checker

Frequently Asked Questions

Find Quick Answers

What is an LFSR?
A Linear Feedback Shift Register (LFSR) is a shift register whose input bit is a linear function of its previous state, commonly used in cryptography, pseudo-random number generation, and digital communications.
How do I format polynomial coefficients?
Enter coefficients as a binary string where 1 indicates a tap position (e.g., 1011 for x³ + x + 1) or as hexadecimal prefixed with 0x (e.g., 0xB). The leftmost bit corresponds to the highest degree.
What does 'maximal length' mean?
A maximal-length LFSR produces the longest possible sequence (2ⁿ-1 bits) before repeating, where n is the degree. The tool checks if your polynomial is primitive to determine this.
Can I simulate large LFSRs?
Yes, but for performance reasons, the tool limits simulations to 1000 steps. For larger sequences, reduce the step count or use specialized software.

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