Compteur modulo 6
Un article de Wikipedia.
(Différences entre les versions)
(→Matrice de référence) |
(→Réduction des fonctions J et K) |
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{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| - | ! | + | !Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 |
|- | |- | ||
| - | ! | + | !0 |
|align="center"|1||align="center"|x||align="center"|x||align="center"|1 | |align="center"|1||align="center"|x||align="center"|x||align="center"|1 | ||
|- | |- | ||
| - | ! | + | !1 |
|align="center"|1||align="center"|x||align="center"|x||align="center"|1 | |align="center"|1||align="center"|x||align="center"|x||align="center"|1 | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|1||align="center"|x||align="center"|-||align="center"|- | ||
|} | |} | ||
</td> | </td> | ||
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{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| - | ! | + | !Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 |
|- | |- | ||
| - | ! | + | !0 |
|align="center"|x||align="center"|1||align="center"|1||align="center"|x | |align="center"|x||align="center"|1||align="center"|1||align="center"|x | ||
|- | |- | ||
| - | ! | + | !1 |
|align="center"|x||align="center"|1||align="center"|1||align="center"|x | |align="center"|x||align="center"|1||align="center"|1||align="center"|x | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|x||align="center"|1||align="center"|-||align="center"|- | ||
|} | |} | ||
</td> | </td> | ||
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{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| - | ! | + | !Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 |
|- | |- | ||
| - | ! | + | !0 |
|align="center"|0||align="center"|1||align="center"|x||align="center"|x | |align="center"|0||align="center"|1||align="center"|x||align="center"|x | ||
|- | |- | ||
| - | ! | + | !1 |
|align="center"|0||align="center"|1||align="center"|x||align="center"|x | |align="center"|0||align="center"|1||align="center"|x||align="center"|x | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|0||align="center"|0||align="center"|-||align="center"|- | ||
|} | |} | ||
</td><td>'''J<sub>b</sub> = Q<sub>a</sub>/Q<sub>d</sub>'''</td><td> </td> | </td><td>'''J<sub>b</sub> = Q<sub>a</sub>/Q<sub>d</sub>'''</td><td> </td> | ||
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{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| - | ! | + | !Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 |
|- | |- | ||
| - | ! | + | !0 |
|align="center"|x||align="center"|x||align="center"|1||align="center"|0 | |align="center"|x||align="center"|x||align="center"|1||align="center"|0 | ||
|- | |- | ||
| - | ! | + | !1 |
|align="center"|x||align="center"|x||align="center"|1||align="center"|0 | |align="center"|x||align="center"|x||align="center"|1||align="center"|0 | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|x||align="center"|x||align="center"|-||align="center"|- | ||
|} | |} | ||
</td><td>'''K<sub>b</sub> = Q<sub>a</sub></td> | </td><td>'''K<sub>b</sub> = Q<sub>a</sub></td> | ||
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{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| - | ! | + | !Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 |
|- | |- | ||
| - | ! | + | !0 |
|align="center"|0||align="center"|0||align="center"|1||align="center"|0 | |align="center"|0||align="center"|0||align="center"|1||align="center"|0 | ||
|- | |- | ||
| - | ! | + | !1 |
|align="center"|x||align="center"|x||align="center"|x||align="center"|x | |align="center"|x||align="center"|x||align="center"|x||align="center"|x | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|0||align="center"|0||align="center"|-||align="center"|- | ||
|} | |} | ||
</td><td>'''J<sub>c</sub> = Q<sub>a</sub>Q<sub>b</sub>'''</td><td> </td> | </td><td>'''J<sub>c</sub> = Q<sub>a</sub>Q<sub>b</sub>'''</td><td> </td> | ||
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{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| - | ! | + | !Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 |
|- | |- | ||
| - | ! | + | !0 |
|align="center"|x||align="center"|x||align="center"|x||align="center"|x | |align="center"|x||align="center"|x||align="center"|x||align="center"|x | ||
|- | |- | ||
| - | ! | + | !1 |
|align="center"|0||align="center"|0||align="center"|1||align="center"|0 | |align="center"|0||align="center"|0||align="center"|1||align="center"|0 | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|x||align="center"|x||align="center"|-||align="center"|- | ||
|} | |} | ||
</td><td>'''K<sub>c</sub> = Q<sub>a</sub>Q<sub>b</sub> = J<sub>c</sub>'''</td> | </td><td>'''K<sub>c</sub> = Q<sub>a</sub>Q<sub>b</sub> = J<sub>c</sub>'''</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td> | ||
| - | {| border="1" cellpadding="5" cellspacing="0" | ||
| - | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 | ||
| - | |- | ||
| - | !00 | ||
| - | |align="center"|0||align="center"|0||align="center"|0||align="center"|0 | ||
| - | |- | ||
| - | !01 | ||
| - | |align="center"|0||align="center"|0||align="center"|1||align="center"|0 | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|x||align="center"|x||align="center"|x||align="center"|x | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|x||align="center"|x||align="center"|x||align="center"|x | ||
| - | |} | ||
| - | </td><td>'''J<sub>d</sub> = Q<sub>a</sub>Q<sub>b</sub>Q<sub>c</sub>'''</td><td> </td> | ||
| - | <td> | ||
| - | {| border="1" cellpadding="5" cellspacing="0" | ||
| - | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub>\Q<sub>b</sub>Q<sub>a</sub>!!00!!01!!11!!10 | ||
| - | |- | ||
| - | !00 | ||
| - | |align="center"|x||align="center"|x||align="center"|x||align="center"|x | ||
| - | |- | ||
| - | !01 | ||
| - | |align="center"|x||align="center"|x||align="center"|x||align="center"|x | ||
| - | |- | ||
| - | !11 | ||
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| - | |- | ||
| - | !10 | ||
| - | |align="center"|0||align="center"|1||align="center"|-||align="center"|- | ||
| - | |} | ||
| - | </td><td>'''K<sub>d</sub> = Q<sub>a</sub>'''</td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
Version du 28 février 2009 à 10:38
Sommaire |
Compteur modulo 6
But
Déterminer les composants logiques d'un compteur modulo 6.
Introduction
Voir le compteur modulo 16.
Compteur modulo 6
Un compteur modulo 6 utilise aussi 3 bascules JK.
Etats du compteur
En se basant sur les informations du compteur modulo 16, les états deviennent les suivants :
| Etat | Q | Q+ | c | b | a | |||||||
| c | b | a | c | b | a | J | K | J | K | J | K | |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | x | 0 | x | 1 | x |
| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | x | 1 | x | x | 1 |
| 2 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | x | x | 0 | 1 | x |
| 3 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | x | x | 1 | x | 1 |
| 4 | 1 | 0 | 0 | 1 | 0 | 1 | x | 0 | 0 | x | 1 | x |
| 5 | 1 | 0 | 1 | 0 | 0 | 0 | x | 1 | 0 | x | x | 1 |
Matrice de référence
La matrice de référence des états du compteur :
| Qc\QbQa | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 0 | 0 | 1 | 3 | 2 |
| 1 | 4 | 5 | - | - |
Réduction des fonctions J et K
Par rapport au compteur modulo 16, seul Kd et Jb changent :
|
Ja = 1 |
|
Ka = 1 = Ja | |||||||||||||||||||||||||||||||
| Jb = Qa/Qd |
| Kb = Qa | |||||||||||||||||||||||||||||||
| Jc = QaQb |
| Kc = QaQb = Jc |
