LFSR Maximal Period Calculator
Compute maximum period of a Linear-Feedback Shift Register (LFSR) and list maximal-length tap polynomials for common bit widths.
How to Use
- Enter number of shift register bits (width).
- Tool returns maximal period 2^N - 1 and a standard maximum-length polynomial.
Show Work
Max-Length Taps
History of the LFSR
Solomon Golomb's 1967 book Shift Register Sequences codified the theory of linear-feedback shift register pseudo-random sequences, building on Marsh and Zierler's 1940s work on maximal-length polynomials. CCSDS standardized PRBS-7, PRBS-15, PRBS-23, and PRBS-31 for spacecraft telemetry in the 1970s. LFSRs became ubiquitous in consumer electronics as CRC generators (Ethernet's CRC-32 uses a 32-bit LFSR) and as PN-code generators in CDMA cellular and GPS.
About This Calculator
Enter register width N (2-32 bits). The tool returns maximal period 2^N − 1, a standard max-length tap pair (from the Zierler-Brillhart tables), and the corresponding polynomial in hex.
LFSRs are everywhere in digital systems: CRC computation, pseudo-random test patterns (PRBS-7 through PRBS-31), spread-spectrum chipping codes, and legacy hardware PRNGs. For cryptographic randomness, LFSRs alone are too predictable — use cryptographic PRNGs (ChaCha20, AES-CTR-DRBG). Everything runs client-side.
About the LFSR Maximal Period Calculator
The LFSR Maximal Period Calculator is a free tool for electronics and circuit design. It runs right in your web browser, so there is nothing to download. Compute maximum period of a Linear-Feedback Shift Register (LFSR) and list maximal-length tap polynomials for common bit widths.
How it works
Type your numbers into the boxes. The answer shows up right away — you do not have to press a button. If you change a number, the answer changes too. So you can try different numbers and watch what happens, or check an answer you worked out yourself. Just make sure each box has the right kind of number in it.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What is an LFSR?
Linear-Feedback Shift Register: a shift register with XOR feedback taps. Produces pseudo-random binary sequences. Core of CRC generators, pseudo-noise sequences for spread-spectrum, and simple hardware PRNGs.
Maximal length?
An N-bit LFSR produces at most 2^N - 1 unique states before repeating (the all-zero state is excluded). A maximal-length tap polynomial hits all 2^N - 1 states in a single cycle.
Uses?
Pseudo-noise sequence generation (GPS C/A code uses 10-bit LFSR giving 1023-chip sequence). CRC code generation. Simple hardware random-number sources. Bit-error-rate test pattern generation.
How do I use the LFSR Maximal Period Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
GPS C/A Code
10-bit LFSR × 2, XOR gives 1023-chip Gold code per satellite.
PRBS Tester
PRBS-7 (2^7 − 1 = 127 bit pattern) for Ethernet BER test.
CRC-32
32-bit LFSR with polynomial 0x04C11DB7 — Ethernet CRC.
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