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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+x5+x4+x3+1
| Sequence #1 (Starting with 0) |
| States: 0 0 forever... |
| Sequence #2 (Starting with 1) |
| States: 1 128 64 32 144 200 228 242 121 60 158 79 39 19 9 4 2 1 |
| Period = 17 (autocorrelation)
Output = 10000000100111100... |
| Sequence #3 (Starting with 3) |
| States: 3 129 192 96 176 88 44 22 139 69 162 209 104 52 26 13 6 3 |
| Period = 17 (autocorrelation)
Output = 11000000110100010... |
| Sequence #4 (Starting with 5) |
| States: 5 130 65 160 208 232 116 58 157 206 231 115 185 92 46 23 11 5 |
| Period = 17 (autocorrelation)
Output = 10100000101110011... |
| Sequence #5 (Starting with 7) |
| States: 7 131 193 224 240 120 188 222 111 183 219 237 246 123 61 30 15 7 |
| Period = 17 (autocorrelation)
Output = 11100000111101101... |
| Sequence #6 (Starting with 8) |
| States: 8 132 66 33 16 136 196 98 177 216 108 54 27 141 70 35 17 8 |
| Period = 17 (autocorrelation)
Output = 00010000100011011... |
| Sequence #7 (Starting with 10) |
| States: 10 133 194 97 48 24 12 134 67 161 80 168 84 170 85 42 21 10 |
| Period = 17 (autocorrelation)
Output = 01010000110000101... |
| Sequence #8 (Starting with 14) |
| States: 14 135 195 225 112 56 156 78 167 83 41 148 202 229 114 57 28 14 |
| Period = 17 (autocorrelation)
Output = 01110000111001010... |
| Sequence #9 (Starting with 18) |
| States: 18 137 68 34 145 72 164 210 233 244 122 189 94 47 151 75 37 18 |
| Period = 17 (autocorrelation)
Output = 01001000100101111... |
| Sequence #10 (Starting with 20) |
| States: 20 138 197 226 241 248 252 254 255 127 63 31 143 71 163 81 40 20 |
| Period = 17 (autocorrelation)
Output = 00101000111111110... |
| Sequence #11 (Starting with 25) |
| States: 25 140 198 99 49 152 76 166 211 105 180 90 45 150 203 101 50 25 |
| Period = 17 (autocorrelation)
Output = 10011000110010110... |
| Sequence #12 (Starting with 29) |
| States: 29 142 199 227 113 184 220 110 55 155 205 102 179 217 236 118 59 29 |
| Period = 17 (autocorrelation)
Output = 10111000111011001... |
| Sequence #13 (Starting with 36) |
| States: 36 146 201 100 178 89 172 86 171 213 106 53 154 77 38 147 73 36 |
| Period = 17 (autocorrelation)
Output = 00100100110101011... |
| Sequence #14 (Starting with 43) |
| States: 43 149 74 165 82 169 212 234 117 186 221 238 119 187 93 174 87 43 |
| Period = 17 (autocorrelation)
Output = 11010100101011101... |
| Sequence #15 (Starting with 51) |
| States: 51 153 204 230 243 249 124 190 223 239 247 251 125 62 159 207 103 51 |
| Period = 17 (autocorrelation)
Output = 11001100111110111... |
| Sequence #16 (Starting with 91) |
| States: 91 173 214 235 245 250 253 126 191 95 175 215 107 181 218 109 182 91 |
| Period = 17 (autocorrelation)
Output = 11011010111111010... |
| Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates. | 
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2024-04-29 00:40:04 ADT
Last Updated: 2014-01-13 |
Richard Tervo [ tervo@unb.ca ] | Back to the course homepage... |