
	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+x⁴+x³+x²+x+1

The circuit taps correspond to P(x) = (101011111).

Taps: (101011111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000010100101010100010111011101011100100111011000010110001111
1101101011001101101110000111000110101001111100010000110010100000
0111101111111100111001100111100101101001101000111010010000011011
110101011011001000100100101111101000010011000101011110000010001...

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 03:20:09 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...