
	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+x²+x+1

The circuit taps correspond to P(x) = (111100111).

Taps: (111100111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

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

Period = 255 (Maximum Length Sequence) (autocorrelation)
Output =
1000000011001111101000110110101010110100110001010010010001000111
0100101000101111010111110010000100000100110111001101000000101010
0001110010110111111110111010100111101101100110010011101111001110
001111000010110001100001101011001010111000001111110001001011101...

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 21:22:33 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...