UNB ECE4253 Digital Communications
Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Linear Recursive Sequence Generator

Shift registers with feedback essentially divide polynomials to create distinctive binary sequences.

This online tool draws and analyzes digital circuits which generate Linear Recursive Sequences (LRS) based on a defining polynomial P(x). The circuit shown below is traced through all possible states. Maximum length sequences are identified. The autocorrelation of each sequence can also be checked (maximum 1023 bits).

Fibonacci Implementation

* alternate configuration
Circuit based on P(x) = x3+x+1

The circuit taps correspond to P(x) = (1011).
Taps: (1011) (prime)
Sequence #1 (Starting with 0)
States: 0 0 forever...

Sequence #2 (Starting with 1)
States: 1 4 2 5 6 7 3 1
Period = 7 (Maximum Length Sequence) (autocorrelation)
Output = 1001011...

See a detailed analysis and State Table for this circuit.

Specify the taps for your sequence

Binary Value:    Discussion   MATLAB

Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates.

2024-06-17 14:56:44 ADT
Last Updated: 2014-01-13
Richard Tervo [ tervo@unb.ca ] Back to the course homepage...