
	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+1

The circuit taps correspond to P(x) = (10111001).

Taps: (10111001) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000101100000111010000100111000110100100101110110111001101100
101011010111110111100001100010001010011001111010101000111111100...

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 23:42:08 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...