
	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+x⁶+x⁴+x+1

The circuit taps correspond to P(x) = (11010011).

Taps: (11010011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000111010100010111000111101110110101111111010011000011010000
101001011011001010101100010000010011111001110010010001100110111...

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 00:00:12 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...