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Unformatted text preview: valid. 1 2. (1.4 # 31, 15 points ) For the circuit corresponding to the Boolean expression ( âˆ¼ P âˆ§ âˆ¼ Q ) âˆ¨ ( âˆ¼ P âˆ§ Q ) âˆ¨ ( P âˆ§ âˆ¼ Q ) there is an equivalent circuit with at most two logic gates. Find such a circuit. Solution: Using the logical equivalences from Theorem 1.1.1, we can reduce the given Boolean expression as follows. ( âˆ¼ P âˆ§ âˆ¼ Q ) âˆ¨ ( âˆ¼ P âˆ§ Q ) âˆ¨ ( P âˆ§ âˆ¼ Q ) â‰¡ h âˆ¼ P âˆ§ ( âˆ¼ Q âˆ¨ Q ) i âˆ¨ ( P âˆ§ âˆ¼ Q ) Distribution Law â‰¡ ( âˆ¼ P âˆ§ T ) âˆ¨ ( P âˆ§ âˆ¼ Q ) Negation Law â‰¡ âˆ¼ P âˆ¨ ( P âˆ§ âˆ¼ Q ) Identity Law â‰¡ ( âˆ¼ P âˆ¨ P ) âˆ§ ( âˆ¼ P âˆ¨ âˆ¼ Q ) Distribution Law â‰¡ T âˆ§ ( âˆ¼ P âˆ¨ âˆ¼ Q ) Negation Law â‰¡ âˆ¼ P âˆ¨ âˆ¼ Q Identity Law â‰¡ âˆ¼ ( P âˆ§ Q ) DeMorganâ€™s Law The corresponding circuit for the Boolean expression âˆ¼ ( P âˆ§ Q ) is given by: P Q 2...
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 Fall '04
 Briggs
 Math, Logic, critical row, Distribution Law Negation Law Identity Law Distribution Law Negation Law Identity Law

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