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Boolean Logic and Circuits ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning

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311_022 Logic Gates

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311_033 Exclusive-OR (XOR)

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Boolean Algebra 311_024 Identity laws: 1. X + 0 = X1D. X 1 = X 2. X + 1 = 12D. X 0 = 0 Idempotent laws: 3. X + X = X3D. X X = X Involution law: 4. (X')' = X Laws of complements: 5. X + X' = 15D. X X' = 0

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Boolean Algebra 311_025 Commutative laws: 6. X + Y = Y + X 6D. XY = YX Associative laws: 7. (X + Y) + Z = X + (Y + Z) 7D. (XY)Z = X(YZ) = XYZ Distributive laws: 8. X(Y + Z) = XY + XZ 8D. X + YZ = (X + Y)(X + Z) DeMorgan's laws: 9. (X + Y )' = X'Y' 12D. (XY)' = X' + Y' Simplification theorem: 10. XY + XY' = X(Adjacency Theorem)

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Minterms and Maxterms 311_046

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Sum of Products (SOP) 311_027 AB' + CD'E + AC'E'

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Product of Sums (POS) 311_028 (A + B')(C + D' + E)(A + C ' + E ' )

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311_07 NAND and NOR Gates 9

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DeMorgan's Laws (X ∙ Y)' = X' + Y' (X + Y)' = X' ∙ Y' 311_0710

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311_07 SOP to NAND-NAND G = WXY + YZ 11

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