
	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+x⁵+x⁴+x²+x+1

The circuit taps correspond to P(x) = (11110111).

Taps: (11110111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000110010100011100001111100010110110011000110100110111111101
110011110100000101011110010010001000010011101101010100101110101...

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 17:17:37 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...