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Basic Digital Design Discussion D2.3

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Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

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Exclusive-OR Gate XOR X Y Z Z = X xor Y X Y Z 0 0 0 0 1 1 1 0 1 1 1 0

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Sum of Products Design X Y minterms 0 0 m0 = X'Y' 0 1 m1 = X'Y 1 0 m2 = XY' 1 1 m3 = XY

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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 = XY' Z = m1 + m2 = (X'Y) + (XY')

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Precedence of Logical Operators All not operations are done first All and operations are done next All or operations are done last Z = (X'Y) + (XY') = X'Y + XY'

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Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

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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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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 = XY' M2 = m2' = X' + Y 1 1 m3 = XY M3 = m3' = X' + Y'

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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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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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Inverses and Duals X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 M0 = X + Y M3 = X' + Y' Z = M0 * M3 = (X + Y)(X' + Y') Z' = m0 + m3 = (X'Y') + (XY) Inverted Duals Z' = M1 * M2 = (X + Y')(X' + Y) Z = m1 + m2 = (X'Y) + (XY') Inverted Duals Equal

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