
	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+x³+x²+1

The circuit taps correspond to P(x) = (10011101).

Taps: (10011101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000100111111100010101011110011001010001000110000111101111101
011010100110110011101101110100100101100011100100001011100000110...

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 21:39:31 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...