
	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+x⁷+x⁶+x³+x²+x+1

The circuit taps correspond to P(x) = (111001111).

Taps: (111001111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000011011101001000111111000001110101001101011000011000110100
0011110001110011110111001001100110110111100101011101111111101101
0011100001010100000010110011101100100000100001001111101011110100
010100101110001000100100101000110010110101010110110001011111001...

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 17:37:16 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...