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ECE4253 Digital Communications |
| Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada | |
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).
alternate configuration
Circuit based on P(x) = x8+x7+x5+x4+1
| Sequence #1 (Starting with 0) |
| States: 0 0 forever... |
| Sequence #2 (Starting with 1) |
| States: 1 128 192 224 112 56 28 142 199 99 49 152 76 38 147 201 100 178 217 236 118 59 157 206 231 243 121 188 222 111 55 155 205 102 179 89 44 150 75 165 210 105 52 26 141 70 35 17 8 4 2 1 |
| Period = 51 (autocorrelation)
Output = 100000001110001100100110111001111011001101001011000... |
| Sequence #3 (Starting with 3) |
| States: 3 129 64 32 144 72 36 146 73 164 82 169 212 106 181 90 173 214 107 53 154 77 166 83 41 20 138 197 98 177 88 172 86 171 213 234 117 186 221 238 119 187 93 46 151 203 101 50 25 12 6 3 |
| Period = 51 (autocorrelation)
Output = 110000001001001010110101100101000110101011101110100... |
| Sequence #4 (Starting with 5) |
| States: 5 130 193 96 176 216 108 182 219 237 246 251 125 190 223 239 247 123 189 94 175 215 235 245 122 61 158 79 167 211 233 244 250 253 126 63 159 207 103 51 153 204 230 115 185 92 174 87 43 21 10 5 |
| Period = 51 (autocorrelation)
Output = 101000001101101111101111010111100101111110011001110... |
| Sequence #5 (Starting with 7) |
| States: 7 131 65 160 80 168 84 170 85 42 149 202 229 242 249 124 62 31 15 135 67 161 208 104 180 218 109 54 27 13 134 195 97 48 24 140 198 227 241 120 60 30 143 71 163 209 232 116 58 29 14 7 |
| Period = 51 (autocorrelation)
Output = 111000001010101001111100001011011000011000111100010... |
| Sequence #6 (Starting with 9) |
| States: 9 132 194 225 240 248 252 254 255 127 191 95 47 23 11 133 66 33 16 136 196 226 113 184 220 110 183 91 45 22 139 69 162 81 40 148 74 37 18 137 68 34 145 200 228 114 57 156 78 39 19 9 |
| Period = 51 (autocorrelation)
Output = 100100001111111101000010001110110100010100100010011... |
| Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates. | 
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2024-04-29 01:45:34 ADT
Last Updated: 2014-01-13 |
Richard Tervo [ tervo@unb.ca ] | Back to the course homepage... |