
	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+x⁵+x⁴+x²+1

The circuit taps correspond to P(x) = (111110101).

Taps: (111110101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000011000100000111101010001100100001011111010010010001001101
1010101111011000001001011100010110010110100111100110011100111111
1101111000000101001100001000111110010101100011100001110110110011
010110111111000110100001101110010011101011101110100010101010010...

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 21:18:54 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...