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). A complete state table is derived for the sequential circuit shown below.
Circuit based on P(x) = x7+x3+x2+x+1
THIS STATE | ⇒ | NEXT STATE | ||
0 0 0 0 0 0 0 | 0 | ⇒ | 0 0 0 0 0 0 0 | 0 |
0 0 0 0 0 0 1 | 1 | ⇒ | 1 0 0 0 0 0 0 | 64 |
0 0 0 0 0 1 0 | 2 | ⇒ | 1 0 0 0 0 0 1 | 65 |
0 0 0 0 0 1 1 | 3 | ⇒ | 0 0 0 0 0 0 1 | 1 |
0 0 0 0 1 0 0 | 4 | ⇒ | 1 0 0 0 0 1 0 | 66 |
0 0 0 0 1 0 1 | 5 | ⇒ | 0 0 0 0 0 1 0 | 2 |
0 0 0 0 1 1 0 | 6 | ⇒ | 0 0 0 0 0 1 1 | 3 |
0 0 0 0 1 1 1 | 7 | ⇒ | 1 0 0 0 0 1 1 | 67 |
0 0 0 1 0 0 0 | 8 | ⇒ | 1 0 0 0 1 0 0 | 68 |
0 0 0 1 0 0 1 | 9 | ⇒ | 0 0 0 0 1 0 0 | 4 |
0 0 0 1 0 1 0 | 10 | ⇒ | 0 0 0 0 1 0 1 | 5 |
0 0 0 1 0 1 1 | 11 | ⇒ | 1 0 0 0 1 0 1 | 69 |
0 0 0 1 1 0 0 | 12 | ⇒ | 0 0 0 0 1 1 0 | 6 |
0 0 0 1 1 0 1 | 13 | ⇒ | 1 0 0 0 1 1 0 | 70 |
0 0 0 1 1 1 0 | 14 | ⇒ | 1 0 0 0 1 1 1 | 71 |
0 0 0 1 1 1 1 | 15 | ⇒ | 0 0 0 0 1 1 1 | 7 |
0 0 1 0 0 0 0 | 16 | ⇒ | 0 0 0 1 0 0 0 | 8 |
0 0 1 0 0 0 1 | 17 | ⇒ | 1 0 0 1 0 0 0 | 72 |
0 0 1 0 0 1 0 | 18 | ⇒ | 1 0 0 1 0 0 1 | 73 |
0 0 1 0 0 1 1 | 19 | ⇒ | 0 0 0 1 0 0 1 | 9 |
0 0 1 0 1 0 0 | 20 | ⇒ | 1 0 0 1 0 1 0 | 74 |
0 0 1 0 1 0 1 | 21 | ⇒ | 0 0 0 1 0 1 0 | 10 |
0 0 1 0 1 1 0 | 22 | ⇒ | 0 0 0 1 0 1 1 | 11 |
0 0 1 0 1 1 1 | 23 | ⇒ | 1 0 0 1 0 1 1 | 75 |
0 0 1 1 0 0 0 | 24 | ⇒ | 1 0 0 1 1 0 0 | 76 |
0 0 1 1 0 0 1 | 25 | ⇒ | 0 0 0 1 1 0 0 | 12 |
0 0 1 1 0 1 0 | 26 | ⇒ | 0 0 0 1 1 0 1 | 13 |
0 0 1 1 0 1 1 | 27 | ⇒ | 1 0 0 1 1 0 1 | 77 |
0 0 1 1 1 0 0 | 28 | ⇒ | 0 0 0 1 1 1 0 | 14 |
0 0 1 1 1 0 1 | 29 | ⇒ | 1 0 0 1 1 1 0 | 78 |
0 0 1 1 1 1 0 | 30 | ⇒ | 1 0 0 1 1 1 1 | 79 |
0 0 1 1 1 1 1 | 31 | ⇒ | 0 0 0 1 1 1 1 | 15 |
0 1 0 0 0 0 0 | 32 | ⇒ | 0 0 1 0 0 0 0 | 16 |
0 1 0 0 0 0 1 | 33 | ⇒ | 1 0 1 0 0 0 0 | 80 |
0 1 0 0 0 1 0 | 34 | ⇒ | 1 0 1 0 0 0 1 | 81 |
0 1 0 0 0 1 1 | 35 | ⇒ | 0 0 1 0 0 0 1 | 17 |
0 1 0 0 1 0 0 | 36 | ⇒ | 1 0 1 0 0 1 0 | 82 |
0 1 0 0 1 0 1 | 37 | ⇒ | 0 0 1 0 0 1 0 | 18 |
0 1 0 0 1 1 0 | 38 | ⇒ | 0 0 1 0 0 1 1 | 19 |
0 1 0 0 1 1 1 | 39 | ⇒ | 1 0 1 0 0 1 1 | 83 |
0 1 0 1 0 0 0 | 40 | ⇒ | 1 0 1 0 1 0 0 | 84 |
0 1 0 1 0 0 1 | 41 | ⇒ | 0 0 1 0 1 0 0 | 20 |
0 1 0 1 0 1 0 | 42 | ⇒ | 0 0 1 0 1 0 1 | 21 |
0 1 0 1 0 1 1 | 43 | ⇒ | 1 0 1 0 1 0 1 | 85 |
0 1 0 1 1 0 0 | 44 | ⇒ | 0 0 1 0 1 1 0 | 22 |
0 1 0 1 1 0 1 | 45 | ⇒ | 1 0 1 0 1 1 0 | 86 |
0 1 0 1 1 1 0 | 46 | ⇒ | 1 0 1 0 1 1 1 | 87 |
0 1 0 1 1 1 1 | 47 | ⇒ | 0 0 1 0 1 1 1 | 23 |
0 1 1 0 0 0 0 | 48 | ⇒ | 0 0 1 1 0 0 0 | 24 |
0 1 1 0 0 0 1 | 49 | ⇒ | 1 0 1 1 0 0 0 | 88 |
0 1 1 0 0 1 0 | 50 | ⇒ | 1 0 1 1 0 0 1 | 89 |
0 1 1 0 0 1 1 | 51 | ⇒ | 0 0 1 1 0 0 1 | 25 |
0 1 1 0 1 0 0 | 52 | ⇒ | 1 0 1 1 0 1 0 | 90 |
0 1 1 0 1 0 1 | 53 | ⇒ | 0 0 1 1 0 1 0 | 26 |
0 1 1 0 1 1 0 | 54 | ⇒ | 0 0 1 1 0 1 1 | 27 |
0 1 1 0 1 1 1 | 55 | ⇒ | 1 0 1 1 0 1 1 | 91 |
0 1 1 1 0 0 0 | 56 | ⇒ | 1 0 1 1 1 0 0 | 92 |
0 1 1 1 0 0 1 | 57 | ⇒ | 0 0 1 1 1 0 0 | 28 |
0 1 1 1 0 1 0 | 58 | ⇒ | 0 0 1 1 1 0 1 | 29 |
0 1 1 1 0 1 1 | 59 | ⇒ | 1 0 1 1 1 0 1 | 93 |
0 1 1 1 1 0 0 | 60 | ⇒ | 0 0 1 1 1 1 0 | 30 |
0 1 1 1 1 0 1 | 61 | ⇒ | 1 0 1 1 1 1 0 | 94 |
0 1 1 1 1 1 0 | 62 | ⇒ | 1 0 1 1 1 1 1 | 95 |
0 1 1 1 1 1 1 | 63 | ⇒ | 0 0 1 1 1 1 1 | 31 |
1 0 0 0 0 0 0 | 64 | ⇒ | 0 1 0 0 0 0 0 | 32 |
1 0 0 0 0 0 1 | 65 | ⇒ | 1 1 0 0 0 0 0 | 96 |
1 0 0 0 0 1 0 | 66 | ⇒ | 1 1 0 0 0 0 1 | 97 |
1 0 0 0 0 1 1 | 67 | ⇒ | 0 1 0 0 0 0 1 | 33 |
1 0 0 0 1 0 0 | 68 | ⇒ | 1 1 0 0 0 1 0 | 98 |
1 0 0 0 1 0 1 | 69 | ⇒ | 0 1 0 0 0 1 0 | 34 |
1 0 0 0 1 1 0 | 70 | ⇒ | 0 1 0 0 0 1 1 | 35 |
1 0 0 0 1 1 1 | 71 | ⇒ | 1 1 0 0 0 1 1 | 99 |
1 0 0 1 0 0 0 | 72 | ⇒ | 1 1 0 0 1 0 0 | 100 |
1 0 0 1 0 0 1 | 73 | ⇒ | 0 1 0 0 1 0 0 | 36 |
1 0 0 1 0 1 0 | 74 | ⇒ | 0 1 0 0 1 0 1 | 37 |
1 0 0 1 0 1 1 | 75 | ⇒ | 1 1 0 0 1 0 1 | 101 |
1 0 0 1 1 0 0 | 76 | ⇒ | 0 1 0 0 1 1 0 | 38 |
1 0 0 1 1 0 1 | 77 | ⇒ | 1 1 0 0 1 1 0 | 102 |
1 0 0 1 1 1 0 | 78 | ⇒ | 1 1 0 0 1 1 1 | 103 |
1 0 0 1 1 1 1 | 79 | ⇒ | 0 1 0 0 1 1 1 | 39 |
1 0 1 0 0 0 0 | 80 | ⇒ | 0 1 0 1 0 0 0 | 40 |
1 0 1 0 0 0 1 | 81 | ⇒ | 1 1 0 1 0 0 0 | 104 |
1 0 1 0 0 1 0 | 82 | ⇒ | 1 1 0 1 0 0 1 | 105 |
1 0 1 0 0 1 1 | 83 | ⇒ | 0 1 0 1 0 0 1 | 41 |
1 0 1 0 1 0 0 | 84 | ⇒ | 1 1 0 1 0 1 0 | 106 |
1 0 1 0 1 0 1 | 85 | ⇒ | 0 1 0 1 0 1 0 | 42 |
1 0 1 0 1 1 0 | 86 | ⇒ | 0 1 0 1 0 1 1 | 43 |
1 0 1 0 1 1 1 | 87 | ⇒ | 1 1 0 1 0 1 1 | 107 |
1 0 1 1 0 0 0 | 88 | ⇒ | 1 1 0 1 1 0 0 | 108 |
1 0 1 1 0 0 1 | 89 | ⇒ | 0 1 0 1 1 0 0 | 44 |
1 0 1 1 0 1 0 | 90 | ⇒ | 0 1 0 1 1 0 1 | 45 |
1 0 1 1 0 1 1 | 91 | ⇒ | 1 1 0 1 1 0 1 | 109 |
1 0 1 1 1 0 0 | 92 | ⇒ | 0 1 0 1 1 1 0 | 46 |
1 0 1 1 1 0 1 | 93 | ⇒ | 1 1 0 1 1 1 0 | 110 |
1 0 1 1 1 1 0 | 94 | ⇒ | 1 1 0 1 1 1 1 | 111 |
1 0 1 1 1 1 1 | 95 | ⇒ | 0 1 0 1 1 1 1 | 47 |
1 1 0 0 0 0 0 | 96 | ⇒ | 0 1 1 0 0 0 0 | 48 |
1 1 0 0 0 0 1 | 97 | ⇒ | 1 1 1 0 0 0 0 | 112 |
1 1 0 0 0 1 0 | 98 | ⇒ | 1 1 1 0 0 0 1 | 113 |
1 1 0 0 0 1 1 | 99 | ⇒ | 0 1 1 0 0 0 1 | 49 |
1 1 0 0 1 0 0 | 100 | ⇒ | 1 1 1 0 0 1 0 | 114 |
1 1 0 0 1 0 1 | 101 | ⇒ | 0 1 1 0 0 1 0 | 50 |
1 1 0 0 1 1 0 | 102 | ⇒ | 0 1 1 0 0 1 1 | 51 |
1 1 0 0 1 1 1 | 103 | ⇒ | 1 1 1 0 0 1 1 | 115 |
1 1 0 1 0 0 0 | 104 | ⇒ | 1 1 1 0 1 0 0 | 116 |
1 1 0 1 0 0 1 | 105 | ⇒ | 0 1 1 0 1 0 0 | 52 |
1 1 0 1 0 1 0 | 106 | ⇒ | 0 1 1 0 1 0 1 | 53 |
1 1 0 1 0 1 1 | 107 | ⇒ | 1 1 1 0 1 0 1 | 117 |
1 1 0 1 1 0 0 | 108 | ⇒ | 0 1 1 0 1 1 0 | 54 |
1 1 0 1 1 0 1 | 109 | ⇒ | 1 1 1 0 1 1 0 | 118 |
1 1 0 1 1 1 0 | 110 | ⇒ | 1 1 1 0 1 1 1 | 119 |
1 1 0 1 1 1 1 | 111 | ⇒ | 0 1 1 0 1 1 1 | 55 |
1 1 1 0 0 0 0 | 112 | ⇒ | 0 1 1 1 0 0 0 | 56 |
1 1 1 0 0 0 1 | 113 | ⇒ | 1 1 1 1 0 0 0 | 120 |
1 1 1 0 0 1 0 | 114 | ⇒ | 1 1 1 1 0 0 1 | 121 |
1 1 1 0 0 1 1 | 115 | ⇒ | 0 1 1 1 0 0 1 | 57 |
1 1 1 0 1 0 0 | 116 | ⇒ | 1 1 1 1 0 1 0 | 122 |
1 1 1 0 1 0 1 | 117 | ⇒ | 0 1 1 1 0 1 0 | 58 |
1 1 1 0 1 1 0 | 118 | ⇒ | 0 1 1 1 0 1 1 | 59 |
1 1 1 0 1 1 1 | 119 | ⇒ | 1 1 1 1 0 1 1 | 123 |
1 1 1 1 0 0 0 | 120 | ⇒ | 1 1 1 1 1 0 0 | 124 |
1 1 1 1 0 0 1 | 121 | ⇒ | 0 1 1 1 1 0 0 | 60 |
1 1 1 1 0 1 0 | 122 | ⇒ | 0 1 1 1 1 0 1 | 61 |
1 1 1 1 0 1 1 | 123 | ⇒ | 1 1 1 1 1 0 1 | 125 |
1 1 1 1 1 0 0 | 124 | ⇒ | 0 1 1 1 1 1 0 | 62 |
1 1 1 1 1 0 1 | 125 | ⇒ | 1 1 1 1 1 1 0 | 126 |
1 1 1 1 1 1 0 | 126 | ⇒ | 1 1 1 1 1 1 1 | 127 |
1 1 1 1 1 1 1 | 127 | ⇒ | 0 1 1 1 1 1 1 | 63 |
Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates. |
2024-05-14 23:52:00 ADT
Last Updated: 2014-01-13 |
Richard Tervo [ tervo@unb.ca ] | Back to the course homepage... |