
	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 Fibonacci

Circuit based on P(x) = x⁷+x⁶+x⁵+x³+x²+x+1

The circuit taps correspond to P(x) = (11101111).

Taps: (11101111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 64 96 48 88 44 86 107 117 58 93 46 23 75 37 82 41 84 42 85 106 53 90 109 118 59 29 78 39 19 9 4 66 33 16 8 68 34 17 72 36 18 73 100 114 121 60 94 47 87 43 21 10 5 2 65 32 80 104 116 122 61 30 79 103 115 57 92 110 119 123 125 126 127 63 95 111 55 27 77 38 83 105 52 26 13 70 99 49 24 76 102 51 89 108 54 91 45 22 11 69 98 113 120 124 62 31 15 7 67 97 112 56 28 14 71 35 81 40 20 74 101 50 25 12 6 3 1

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000110101110100101010110111001000010001001001111010100000101
111001110111111101100101100011001101101000111110000111000101001...

See a detailed analysis and State Table for this circuit.

Specify the taps for your sequence

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


2024-04-29 02:37:02 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...