
	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+x⁵+x²+x+1

The circuit taps correspond to P(x) = (10100111).

Taps: (10100111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000101011011111110011011010101000100100110011110001110111010
111101001011001010011100100011000101110000100001101000001111101...

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.


2024-04-28 22:01:53 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...