
	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+1

The circuit taps correspond to P(x) = (11000001).

Taps: (11000001) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000111111101010100110011101110100101100011011110110101101100
100100011100001011111001010111001101000100111100010100001100000...

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 19:44:59 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...