
	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+x³+x+1

The circuit taps correspond to P(x) = (11001011).

Taps: (11001011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000111101100110001001001110011111001000001000110101010011011
010010100001011000011001011111110101101110111100011101000101011...

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 18:46:51 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...