
	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+x²+1

The circuit taps correspond to P(x) = (11100101).

Taps: (11100101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000110111110000010110000100001110100011000100111001010011010
010111101011101110001111001100100100010101011011001111111011010...

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 20:41:22 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...