
	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+x³+x²+1

The circuit taps correspond to P(x) = (11111101).

Taps: (11111101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 127 (Maximum Length Sequence) (autocorrelation)
Output =
1000000110000100100111111101111100011101010100101011110100110011
100110101100010001011101100100001111001011011100000101000110110...

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.


2024-04-29 00:00:13 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...