
	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+x³+1

The circuit taps correspond to P(x) = (10001001).

Taps: (10001001) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000100010011000101110101101100000110011010100111001111011010
000101010111110100101000110111000111111100001110111100101100100...

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 04:10:56 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...