
	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+x⁴+x³+x²+x+1

The circuit taps correspond to P(x) = (10111111).

Taps: (10111111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000101101100010100000111011010011110000100110111010001000110
101100111001100101111010100101010111000111110111111100100100001...

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 00:41:44 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...