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+10 votes

Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input):

- Write the truth table for all bits. Label the input bits I
_{1}, I_{2}, .... with I_{1}as the least significant bit. Label the output bits R_{1}, R_{2}.... with R_{1}as the least significant bit. Use 1 to signify truth. - Draw one circuit for each output bit using,
, two two-input AND gates, one two-input OR gate and two NOT gates.*altogether*

+8 votes

Best answer

$I_4$ | $I_3$ | $I_2$ | $I_1$ | $R_3$ | $R_2$ | $R_1$ | |
---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 |

0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 |

0 | 0 | 1 | 0 | 2 |
0 | 1 | 0 |

0 | 0 | 1 | 1 | 3 |
0 | 1 | 1 |

0 | 1 | 0 | 0 | 4 |
1 | 0 | 0 |

0 | 1 | 0 | 1 | 5 |
1 | 0 | 1 |

0 | 1 | 1 | 0 | 6 |
0 | 0 | 0 |

0 | 1 | 1 | 1 | 7 |
0 | 0 | 1 |

1 | 0 | 0 | 0 | 8 |
0 | 1 | 0 |

1 | 0 | 0 | 1 | 9 |
0 | 1 | 1 |

$R_1 = I_1$

$R_2 = I_2\overline{ I_3} + I_4$

$R_3 = I_3\overline{I_2}$

This requires $2$ NOT gates, $2$ two-input AND gates and $1$ two-input OR gate.

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