
	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) = x⁸+x⁵+x³+x+1

The circuit taps correspond to P(x) = (100101011).

Taps: (100101011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 128 64 32 144 72 164 210 233 244 250 253 254 255 127 63 31 143 199 99 177 88 172 86 171 85 170 213 234 245 122 189 222 111 55 155 205 102 51 153 76 166 83 41 148 74 37 18 137 68 34 17 136 196 98 49 24 140 198 227 241 120 60 30 15 135 67 33 16 8 132 66 161 80 40 20 10 5 130 193 224 240 248 124 62 159 207 231 243 249 252 126 191 95 175 87 43 21 138 69 162 81 168 84 42 149 202 101 50 25 12 134 195 97 48 152 204 230 115 185 220 238 247 251 125 190 223 239 119 187 93 46 151 75 165 82 169 212 106 181 90 45 150 203 229 114 57 156 206 103 179 217 108 54 27 141 70 163 209 232 116 186 221 110 183 219 237 246 123 61 158 79 167 211 105 180 218 109 182 91 173 214 235 117 58 157 78 39 147 73 36 146 201 100 178 89 44 22 139 197 226 113 56 28 142 71 35 145 200 228 242 121 188 94 47 23 11 133 194 225 112 184 92 174 215 107 53 26 13 6 131 65 160 208 104 52 154 77 38 19 9 4 2 129 192 96 176 216 236 118 59 29 14 7 3 1

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000010010111111110001101010101111011001100101001000100011000
1111000010000101000001111100111111010100010101001100001100111011
1110111010010101101001110011011000101110110111100101101101011100
100100110100011100010011110100001110101100000101100100000011011...

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 16:38:51 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...