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| | == Résultats == | | == Résultats == |
| - | <logicsim height="1100" width="1000" circuit="Decompteurmodulo24.lsim" start="true" /> | + | <logicsim height="1100" width="1100" circuit="Decompteurmodulo24.lsim" start="true" /> |
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| | == Conclusions == | | == Conclusions == |
Version actuelle
Décompteur modulo 24
But
Déterminer les composants logiques d'un décompteur modulo 24.
Introduction
Voir le compteur modulo 16.
Décompteur modulo 24
Un décompteur modulo 24 nécessite 6 bascules JK.
Etats du décompteur
Les états d'un décompteur modulo 24 sont les suivants :
| Etat | Q | Q+ | f | e | d | c | b | a
|
| f | e | d | c | b | a | f | e | d | c | b | a | J | K | J | K | J | K | J | K | J | K | J | K
|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | x | 0 | x | 0 | x | 0 | x | 1 | x | 1 | x
|
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | x | 0 | x | 0 | x | 0 | x | 0 | x | x | 1
|
| 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | x | 1 | 1 | x
|
| 3 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | x | 0 | x | 0 | x | 0 | x | x | 0 | x | 1
|
| 4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | x | 0 | x | 0 | x | x | 1 | 1 | x | 1 | x
|
| 5 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | x | 0 | x | 0 | x | x | 0 | 0 | x | x | 1
|
| 6 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | x | 1 | 1 | x
|
| 7 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | x | 0 | x | 0 | x | x | 0 | x | 0 | x | 1
|
| 8 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | x | 0 | x | x | 1 | 1 | x | 1 | x | 1 | x
|
| 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | x | 0 | x | x | 0 | 0 | x | 0 | x | x | 1
|
| 10 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | x | x | 1 | 1 | x | 0 | x | 0 | x | 1 | x
|
| 11 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | x | x | 0 | 0 | x | 0 | x | 0 | x | x | 1
|
| 12 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | x | 1 | 1 | x
|
| 13 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | x | x | 0 | 0 | x | 0 | x | x | 0 | x | 1
|
| 14 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | x | x | 0 | 0 | x | x | 1 | 1 | x | 1 | x
|
| 15 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | x | x | 0 | 0 | x | x | 0 | 0 | x | x | 1
|
| 16 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | x | 1 | 1 | x
|
| 17 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | x | x | 0 | 0 | x | x | 0 | x | 0 | x | 1
|
| 18 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | x | x | 0 | x | 1 | 1 | x | 1 | x | 1 | x
|
| 19 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | x | x | 0 | x | 0 | 0 | x | 0 | x | x | 1
|
| 20 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | x | 1 | 1 | x | 1 | x | 0 | x | 0 | x | 1 | x
|
| 21 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | x | 0 | 0 | x | 0 | x | 0 | x | 0 | x | x | 1
|
| 22 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | x | 0 | 0 | x | 0 | x | 0 | x | x | 1 | 1 | x
|
| 23 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | x | 0 | 0 | x | 0 | x | 0 | x | x | 0 | x | 1
|
Matrice de référence
La matrice de référence des états du décompteur :
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 0 | 1 | 3 | 2 | 6 | 7 | 5 | 4
|
| 001
| 8 | 9 | - | - | - | - | - | -
|
| 011
| 18 | 19 | - | - | - | - | - | -
|
| 010
| 10 | 11 | 13 | 12 | 16 | 17 | 15 | 14
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 20 | 21 | 23 | 22 | - | - | - | -
|
Réduction des fonctions J et K
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 1 | x | x | 1 | 1 | x | x | 1
|
| 001
| 1 | x | - | - | - | - | - | -
|
| 011
| 1 | x | - | - | - | - | - | -
|
| 010
| 1 | x | x | 1 | 1 | x | x | 1
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 1 | x | x | 1 | - | - | - | -
|
|
Ja = 1 | |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| x | 1 | 1 | x | x | 1 | 1 | x
|
| 001
| x | 1 | - | - | - | - | - | -
|
| 011
| x | 1 | - | - | - | - | - | -
|
| 010
| x | 1 | 1 | x | x | 1 | 1 | x
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| x | 1 | 1 | x | - | - | - | -
|
|
Ka = 1 |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 1 | 0 | x | x | x | x | 0 | 1
|
| 001
| 1 | 0 | - | - | - | - | - | -
|
| 011
| 1 | 0 | - | - | - | - | - | -
|
| 010
| 0 | 0 | x | x | x | x | 0 | 1
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 0 | 0 | x | x | - | - | - | -
|
| Jb = /Qa(Qc+Qd+/Qe/Qf) | |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| x | x | 0 | 1 | 1 | 0 | x | x
|
| 001
| x | x | - | - | - | - | - | -
|
| 011
| x | x | - | - | - | - | - | -
|
| 010
| x | x | 0 | 1 | 1 | 0 | x | x
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| x | x | 0 | 1 | - | - | - | -
|
| Kb = /Qa |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 0 | 0 | 0 | 0 | x | x | x | x
|
| 001
| 1 | 0 | - | - | - | - | - | -
|
| 011
| 1 | 0 | - | - | - | - | - | -
|
| 010
| 0 | 0 | 0 | 0 | x | x | x | x
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 0 | 0 | 0 | 0 | - | - | - | -
|
| Jc = /QaQd | |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| x | x | x | x | 0 | 0 | 0 | 1
|
| 001
| x | x | - | - | - | - | - | -
|
| 011
| x | x | - | - | - | - | - | -
|
| 010
| x | x | x | x | 0 | 0 | 0 | 1
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| x | x | x | x | - | - | - | -
|
| Kc = /Qa/Qb |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
|
| 001
| x | x | - | - | - | - | - | -
|
| 011
| x | x | - | - | - | - | - | -
|
| 010
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 1 | 0 | 0 | 0 | - | - | - | -
|
| Jd = /Qa/Qb/Qc(Qe+Qf) | |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| x | x | x | x | x | x | x | x
|
| 001
| 1 | 0 | - | - | - | - | - | -
|
| 011
| 1 | 0 | - | - | - | - | - | -
|
| 010
| x | x | x | x | x | x | x | x
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| x | x | x | x | - | - | - | -
|
| Kd = /Qa |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
|
| 001
| 0 | 0 | - | - | - | - | - | -
|
| 011
| x | x | - | - | - | - | - | -
|
| 010
| x | x | x | x | x | x | x | x
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 1 | 0 | 0 | 0 | - | - | - | -
|
| Je = /Qa/QbQf | |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| x | x | x | x | x | x | x | x
|
| 001
| x | x | - | - | - | - | - | -
|
| 011
| 0 | 0 | - | - | - | - | - | -
|
| 010
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| x | x | x | x | - | - | - | -
|
| Ke = /Qa/Qb/Qc/Qd |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0
|
| 001
| 0 | 0 | - | - | - | - | - | -
|
| 011
| 0 | 0 | - | - | - | - | - | -
|
| 010
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| x | x | x | x | - | - | - | -
|
| Jf = /Qa/Qb/Qc/Qd/Qe | |
| QfQeQd\QcQbQa | 000 | 001 | 011 | 010 | 110 | 111 | 101 | 100
|
| 000
| x | x | x | x | x | x | x | x
|
| 001
| x | x | - | - | - | - | - | -
|
| 011
| x | x | - | - | - | - | - | -
|
| 010
| x | x | x | x | x | x | x | x
|
| 110
| - | - | - | - | - | - | - | -
|
| 111
| - | - | - | - | - | - | - | -
|
| 101
| - | - | - | - | - | - | - | -
|
| 100
| 1 | 0 | 0 | 0 | - | - | - | -
|
| Kf = /Qa/Qb |
Résultats
Conclusions
Ressources
