
	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+1

The circuit taps correspond to P(x) = (11110001).

Taps: (11110001) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000110011011000111001110101110000100110000010101011010010010
100111100100011010100001111111011101101111010001011001011111000...

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 20:24:01 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...