
	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+x⁶+x⁵+x²+1

The circuit taps correspond to P(x) = (101100101).

Taps: (101100101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000010111011110110011111111001011010110111010101011100100110
1101001100110100011101101100010001001111010010010000111100010100
1110001111101011110011101000010101100101000101100000110010001100
001101111110111000010000010010101001011111000000111001100011010...

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 19:18:58 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...