
	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+x⁴+1

The circuit taps correspond to P(x) = (10010001).

Taps: (10010001) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000100100110100111101110000111111100011101100010100101111101
010100001011011110011100101011001100000110110101110100011001000...

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 18:50:45 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...