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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+x6+x4+x2+x+1
| Sequence #1 (Starting with 0) |
| States: 0 0 forever... |
| Sequence #2 (Starting with 1) |
| States: 1 128 192 96 176 88 44 150 75 165 210 105 52 26 13 6 3 1 |
| Period = 17 (autocorrelation)
Output = 10000000110100101... |
| Sequence #3 (Starting with 2) |
| States: 2 129 64 160 208 232 116 186 221 238 119 187 93 46 23 11 5 2 |
| Period = 17 (autocorrelation)
Output = 01000000101110111... |
| Sequence #4 (Starting with 4) |
| States: 4 130 65 32 16 136 196 226 241 120 60 30 143 71 35 17 8 4 |
| Period = 17 (autocorrelation)
Output = 00100000100011110... |
| Sequence #5 (Starting with 7) |
| States: 7 131 193 224 112 56 156 206 103 51 153 204 230 115 57 28 14 7 |
| Period = 17 (autocorrelation)
Output = 11100000111001100... |
| Sequence #6 (Starting with 9) |
| States: 9 132 66 33 144 72 164 82 169 84 170 85 42 149 74 37 18 9 |
| Period = 17 (autocorrelation)
Output = 10010000100101010... |
| Sequence #7 (Starting with 10) |
| States: 10 133 194 225 240 248 252 126 63 31 15 135 67 161 80 40 20 10 |
| Period = 17 (autocorrelation)
Output = 01010000111111000... |
| Sequence #8 (Starting with 12) |
| States: 12 134 195 97 48 152 76 38 19 137 68 34 145 200 100 50 25 12 |
| Period = 17 (autocorrelation)
Output = 00110000110010001... |
| Sequence #9 (Starting with 21) |
| States: 21 138 69 162 81 168 212 106 53 154 205 102 179 89 172 86 43 21 |
| Period = 17 (autocorrelation)
Output = 10101000101011001... |
| Sequence #10 (Starting with 22) |
| States: 22 139 197 98 49 24 140 70 163 209 104 180 218 109 182 91 45 22 |
| Period = 17 (autocorrelation)
Output = 01101000110001011... |
| Sequence #11 (Starting with 27) |
| States: 27 141 198 99 177 216 236 246 251 253 254 255 127 191 223 111 55 27 |
| Period = 17 (autocorrelation)
Output = 11011000110111111... |
| Sequence #12 (Starting with 29) |
| States: 29 142 199 227 113 184 92 174 215 107 181 90 173 214 235 117 58 29 |
| Period = 17 (autocorrelation)
Output = 10111000111010110... |
| Sequence #13 (Starting with 36) |
| States: 36 146 201 228 242 121 188 222 239 247 123 61 158 79 39 147 73 36 |
| Period = 17 (autocorrelation)
Output = 00100100111101111... |
| Sequence #14 (Starting with 41) |
| States: 41 148 202 229 114 185 220 110 183 219 237 118 59 157 78 167 83 41 |
| Period = 17 (autocorrelation)
Output = 10010100111011011... |
| Sequence #15 (Starting with 47) |
| States: 47 151 203 101 178 217 108 54 155 77 166 211 233 244 122 189 94 47 |
| Period = 17 (autocorrelation)
Output = 11110100110110010... |
| Sequence #16 (Starting with 62) |
| States: 62 159 207 231 243 249 124 190 95 175 87 171 213 234 245 250 125 62 |
| Period = 17 (autocorrelation)
Output = 01111100111110101... |
| Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates. | 
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2024-04-28 18:25:39 ADT
Last Updated: 2014-01-13 |
Richard Tervo [ tervo@unb.ca ] | Back to the course homepage... |