1. What is LFSR?

A Linear Feedback Shift Register (LFSR) is a shift register whose input bit is a linear function of its previous state. It's commonly used in digital circuits for pseudo-random number generation, cryptography, and digital communications.

2. How Does the Calculator Work?

The calculator uses the LFSR equation:

Where:

• \( \text{state} \) — Current state of the register (integer)
• \( \text{tap} \) — Tap position that determines the feedback (integer)
• \( \gg \) — Bitwise right shift operator
• \( \oplus \) — Bitwise XOR operator
• \( \& \) — Bitwise AND operator

Explanation: The equation calculates the next state of the LFSR by right-shifting the current state and applying feedback based on the tap position and the least significant bit.

3. Importance of LFSR Calculation

Details: Understanding LFSR operations is crucial for designing pseudo-random number generators, error detection/correction codes, and cryptographic systems.

4. Using the Calculator

Tips: Enter the current state and tap position as integers. The calculator will compute the next state in the sequence.

5. Frequently Asked Questions (FAQ)

Q1: What's the maximum state value I can use?
A: The calculator uses PHP integers, so the maximum depends on your system (typically 32-bit or 64-bit integers).

Q2: How do I choose a good tap position?
A: Tap positions that produce maximal-length sequences are best. Common choices are based on primitive polynomials.

Q3: Can I use this for cryptographic purposes?
A: Simple LFSRs are not cryptographically secure. For security applications, use cryptographic PRNGs.

Q4: What's the difference between Fibonacci and Galois LFSRs?
A: They're mathematically equivalent but implemented differently. This calculator implements the Galois configuration.

Q5: How can I visualize the LFSR sequence?
A: You can run the calculator repeatedly, using each output as the next input, to generate the complete sequence.