Linear Feedback Shift Register Calculator - Generate pseudo-random sequences, understand polynomial feedback, and visualize shift register operations.
Linear Feedback Shift Register is a shift register whose input bit is a linear function of its previous state. Used for generating pseudo-random sequences.
LFSRs generate sequences that appear random but are deterministic. Maximum period for n-bit LFSR is 2ⁿ - 1.
Used in cryptography, digital communications, built-in self-test, scrambling, and error detection (CRC).
Feedback configuration represented by characteristic polynomial. Primitive polynomials give maximal length sequences.
LFSRs are components in stream ciphers (like A5/1 in GSM). Combined LFSRs create more secure sequences.
Efficient in hardware with flip-flops and XOR gates. Used in FPGA designs and ASIC testing.
Polynomial: x⁴ + x + 1
Period: 15 bits
Taps: [4, 1]
Use: Simple PRNG
Polynomial: x⁸ + x⁶ + x⁵ + x⁴ + 1
Period: 255 bits
Taps: [8, 6, 5, 4]
Use: CRC-8
Polynomial: x¹⁶ + x¹⁴ + x¹³ + x¹¹ + 1
Period: 65535 bits
Taps: [16, 14, 13, 11]
Use: CRC-16
Polynomial: x³² + x²² + x² + x¹ + 1
Period: 4.29e9 bits
Taps: [32, 22, 2, 1]
Use: CRC-32