
	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+x⁴+x²+1

The circuit taps correspond to P(x) = (11010101).

Taps: (11010101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000111011011111001111111010010010101110101010011100011001011
001100010111101110010001000011010110100011110000010011011000010...

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 17:18:27 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...