Compteur modulo 24
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" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
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| - | ! | + | !000 |
| - | |align="center"|1||align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
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| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
|} | |} | ||
</td> | </td> | ||
<td>'''J<sub>a</sub> = 1'''</td><td> </td> | <td>'''J<sub>a</sub> = 1'''</td><td> </td> | ||
<td> | <td> | ||
| - | {| border="1" cellpadding="5" cellspacing="0" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
|- | |- | ||
| - | ! | + | !000 |
| - | |align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | ! | + | !001 |
| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | ! | + | !011 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
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| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
|} | |} | ||
</td> | </td> | ||
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| - | {| border="1" cellpadding="5" cellspacing="0" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
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| - | ! | + | !000 |
| - | |align="center"|0||align="center"|1||align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | ! | + | !001 |
| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | ! | + | !011 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | !10 | + | !010 |
| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||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> | ||
<td> | <td> | ||
| - | {| border="1" cellpadding="5" cellspacing="0" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
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| - | ! | + | !000 |
| - | |align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | ! | + | !001 |
| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | ! | + | !011 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||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" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
|- | |- | ||
| - | ! | + | !000 |
| - | |align="center"|0||align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | ! | + | !001 |
| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | ! | + | !011 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | !10 | + | !010 |
| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||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> | ||
<td> | <td> | ||
| - | {| border="1" cellpadding="5" cellspacing="0" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
|- | |- | ||
| - | ! | + | !000 |
| - | |align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | ! | + | !001 |
| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | ! | + | !011 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||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> | ||
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| - | {| border="1" cellpadding="5" cellspacing="0" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| - | !Q<sub>d</sub>Q<sub>c</sub> | + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 |
|- | |- | ||
| - | ! | + | !000 |
| - | |align="center"|0||align="center"| | + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 |
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| - | ! | + | !001 |
| - | |align="center"| | + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | ! | + | !011 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
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| - | |align="center"| | + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 |
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
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| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
|} | |} | ||
</td><td>'''J<sub>d</sub> = Q<sub>a</sub>Q<sub>b</sub>Q<sub>c</sub>'''</td><td> </td> | </td><td>'''J<sub>d</sub> = Q<sub>a</sub>Q<sub>b</sub>Q<sub>c</sub>'''</td><td> </td> | ||
<td> | <td> | ||
| - | {| border="1" cellpadding="5" cellspacing="0" | + | {| align="center" border="1" cellpadding="5" cellspacing="0" |
| + | |- | ||
| + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 | ||
| + | |- | ||
| + | !000 | ||
| + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 | ||
| + | |- | ||
| + | !001 | ||
| + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !011 | ||
| + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !010 | ||
| + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 | ||
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |} | ||
| + | </td><td>'''K<sub>d</sub> = Q<sub>a</sub>'''</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td> | ||
| + | {| align="center" border="1" cellpadding="5" cellspacing="0" | ||
| + | |- | ||
| + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 | ||
| + | |- | ||
| + | !000 | ||
| + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 | ||
| + | |- | ||
| + | !001 | ||
| + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !011 | ||
| + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !010 | ||
| + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 | ||
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |} | ||
| + | </td><td>'''J<sub>d</sub> = Q<sub>a</sub>Q<sub>b</sub>Q<sub>c</sub>'''</td><td> </td> | ||
| + | <td> | ||
| + | {| align="center" border="1" cellpadding="5" cellspacing="0" | ||
| + | |- | ||
| + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 | ||
| + | |- | ||
| + | !000 | ||
| + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 | ||
| + | |- | ||
| + | !001 | ||
| + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !011 | ||
| + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !010 | ||
| + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 | ||
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |} | ||
| + | </td><td>'''K<sub>d</sub> = Q<sub>a</sub>'''</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td> | ||
| + | {| align="center" border="1" cellpadding="5" cellspacing="0" | ||
| + | |- | ||
| + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 | ||
| + | |- | ||
| + | !000 | ||
| + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 | ||
| + | |- | ||
| + | !001 | ||
| + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !011 | ||
| + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !010 | ||
| + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 | ||
| + | |- | ||
| + | !110 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !111 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !101 | ||
| + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !100 | ||
| + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |} | ||
| + | </td><td>'''J<sub>d</sub> = Q<sub>a</sub>Q<sub>b</sub>Q<sub>c</sub>'''</td><td> </td> | ||
| + | <td> | ||
| + | {| align="center" border="1" cellpadding="5" cellspacing="0" | ||
| + | |- | ||
| + | !Q<sub>f</sub>Q<sub>e</sub>Q<sub>d</sub>\Q<sub>c</sub>Q<sub>b</sub>Q<sub>a</sub>!!000!!001!!011!!010!!110!!111!!101!!100 | ||
| + | |- | ||
| + | !000 | ||
| + | |align="center"|0||align="center"|1||align="center"|3||align="center"|2||align="center"|6||align="center"|7||align="center"|5||align="center"|4 | ||
| + | |- | ||
| + | !001 | ||
| + | |align="center"|8||align="center"|9||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
| + | |- | ||
| + | !011 | ||
| + | |align="center"|18||align="center"|19||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- | ||
|- | |- | ||
| - | ! | + | !010 |
| + | |align="center"|10||align="center"|11||align="center"|13||align="center"|12||align="center"|16||align="center"|17||align="center"|15||align="center"|14 | ||
|- | |- | ||
| - | ! | + | !110 |
| - | |align="center"| | + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
|- | |- | ||
| - | ! | + | !111 |
| - | |align="center"| | + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
|- | |- | ||
| - | ! | + | !101 |
| - | |align="center"|-||align="center"|-||align="center"|-||align="center"|- | + | |align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
|- | |- | ||
| - | ! | + | !100 |
| - | |align="center"| | + | |align="center"|20||align="center"|21||align="center"|23||align="center"|22||align="center"|-||align="center"|-||align="center"|-||align="center"|- |
|} | |} | ||
</td><td>'''K<sub>d</sub> = Q<sub>a</sub>'''</td> | </td><td>'''K<sub>d</sub> = Q<sub>a</sub>'''</td> | ||
Version du 9 mars 2009 à 12:16
Sommaire |
Compteur modulo 24
But
Déterminer les composants logiques d'un compteur modulo 24.
Introduction
Voir le compteur modulo 16.
Compteur modulo 24
Un compteur modulo 24 utilise aussi 6 bascules JK.
Etats du compteur
En se basant sur les informations du compteur modulo 16, les états deviennent 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 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x | x | 0 |
| 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x |
| 3 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | x | 0 | x | 0 | x | 1 | x | x | 1 | x | 1 |
| 4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | 0 | x | 1 | x |
| 5 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x | x | 1 |
| 6 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | x | 0 | 1 | x |
| 7 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | x | 0 | x | 1 | x | x | 1 | 1 | x | x | 1 |
| 8 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | x | 0 | x | 1 | x | 0 | x | 0 | x | 1 | x |
| 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | x | 1 | x | x | 1 | 0 | x | 0 | x | x | 1 |
| 10 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | 0 | x | 1 | x |
| 11 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | x | x | 0 | 0 | x | 0 | x | 1 | x | x | 1 |
| 12 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | x | 0 | 1 | x |
| 13 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | x | x | 0 | 0 | x | 1 | x | x | 1 | x | 1 |
| 14 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | 0 | x | 1 | x |
| 15 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | x | x | 0 | 0 | x | x | 0 | 1 | x | x | 1 |
| 16 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | x | 0 | 1 | x |
| 17 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | x | x | 0 | 1 | x | x | 1 | x | 1 | x | 1 |
| 18 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | x | x | 0 | x | 0 | 0 | x | 0 | x | 1 | x |
| 19 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | x | x | 1 | x | 1 | 0 | x | 0 | x | x | 1 |
| 20 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | x | 0 | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x |
| 21 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | x | 0 | 0 | x | 0 | x | 0 | x | 1 | x | x | 1 |
| 22 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | x | 1 | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x |
| 23 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | x | 1 | 0 | x | 0 | x | 0 | x | x | 1 | x | 1 |
Matrice de référence
La matrice de référence des états du compteur :
| 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
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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Jd = QaQbQc |
| Kd = Qa | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Jd = QaQbQc |
| Kd = Qa | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Jd = QaQbQc |
| Kd = Qa |
