
	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+x+1

The circuit taps correspond to P(x) = (10000011).

Taps: (10000011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000100000110000101000111100100010110011101010011111010000111
000100100110110101101111011000110100101110111001100101010111111...

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 00:01:56 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...