
	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+x²+1

The circuit taps correspond to P(x) = (100101101).

Taps: (100101101) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000010010100111111110001100010101010000100001100110000011111
0111011111101010010110101011001110010011001000101110001000111100
1011110000101000110101111100111101100101011101011011100110100110
110100010011101101100001110100100100000101100011100000011011110...

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 16:07:17 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...