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Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Module M1.2 Section 3.2

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Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

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Introduction to Computer Engineering by Richard E. Haskell Exclusive-OR Gate XOR X Y Z Z = X $ Y X Y Z 0 0 0 0 1 1 1 0 1 1 1 0

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Introduction to Computer Engineering by Richard E. Haskell Sum of Products Design X Y minterms 0 0 m0 = !X & !Y 0 1 m1 = !X & Y 1 0 m2 = X & !Y 1 1 m3 = X & Y

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Introduction to Computer Engineering by Richard E. Haskell Sum of Products Design X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate m1 = !X & Y m2 = X & !Y Z = m1 # m2 = (!X & Y) # (X & !Y)

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Introduction to Computer Engineering by Richard E. Haskell Sum of Products: Exclusive-OR !X & Y X & !Y Z = (!X & Y) # (X & !Y)

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Introduction to Computer Engineering by Richard E. Haskell Precedence of Logical Operators All ! operations are done first All & operations are done next All # operations are done last Z = (!X & Y) # (X & !Y) = !X & Y # X & !Y

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Introduction to Computer Engineering by Richard E. Haskell Problem

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Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

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Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design Maxterms: A maxterm is NOT a minterm maxterm M0 = NOT minterm m0 M0 = !m0 = !(!X & !Y) = !!(!!X # !!Y) = X # Y

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Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design X Y minterms maxterms 0 0 m0 = !X & !Y M0 = !m0 = X # Y 0 1 m1 = !X & Y M1 = !m1 = X # !Y 1 0 m2 = X & !Y M2 = !m2 = !X # Y 1 1 m3 = X & Y M3 = !m3 = !X # !Y

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Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate Z is NOT minterm m0 AND it is NOT minterm m3

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Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate M0 = X # Y M3 = !X # !Y Z = M0 & M3 = (X # Y) & (!X # !Y)

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Introduction to Computer Engineering by Richard E. Haskell Product of Sums: Exclusive-OR

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