
	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+x²+x+1

The circuit taps correspond to P(x) = (10001111).

Taps: (10001111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000100011111010011010001011110110111011111110000101011000100
111100101001001011010101000001100100001110101110011100011011001...

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 23:58:40 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...