Question

Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output ((¬p ∨ ¬r) ∧ ¬q) ∨ (¬p ∧ (q ∨ r)) from input bits p, q, and r.

Answer 1

Explanation:

The required combinatorial circuit can be constructed as follows:

Firstly, we need to find the negation of p, q and r which can be achieved using inverters as shown below:

p q r

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NOT NOT NOT

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~p ~q ~r

Next, we can use OR gates to form the term (¬p ∨ ¬r) and (q ∨ r) as shown below:

~p ~r q r

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OR OR | |

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pORr rORp qORr rORq

Then, we can use AND gates to form the terms (¬p ∨ ¬r) ∧ ¬q and ¬p ∧ (q ∨ r) as shown below:

~p ~r q r

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OR OR | |

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pORr rORp qORr rORq

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NOT NOT NOT |

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~q ~pORr ~qORr qORr

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AND OR AND |

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(~pORr ~q) qORr qORr

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OR AND |

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(~pORr ∨ ~q) (~pORr ∧ qORr)

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| OR |

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((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))

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OUTPUT

((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))