
	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+x³+x+1

The circuit taps correspond to P(x) = (10101011).

Taps: (10101011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000101000011011001000001111000101101011000010001001110111101
000110011010011000111001010101110101001001011111110011111011011...

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 03:01:48 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...