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Unformatted text preview: © Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 7: DeMorgan’s Theorem Logic Simplification Circuit Analysis © Mark Redekopp, All rights reserved 2 & 3 Variable Theorems T8 XY+XZ = X(Y+Z) T8’ (X+Y)(X+Z) = X+YZ T9 X + XY = X T9’ X(X+Y) = X T10 XY + XY’ = X T10’ (X+Y)(X+Y’) = X T11 XY + X’Z + YZ = XY + X’Z T11’ (X+Y)(X’+Z)(Y+Z) = (X+Y)(X’+Z) © Mark Redekopp, All rights reserved DeMorgan’s Theorem • Inverting output of an AND gate = inverting the inputs of an OR gate • Inverting output of an OR gate = inverting the inputs of an AND gate A function’s inverse is equivalent to inverting all the inputs and changing AND to OR and vice versa A •B A+B A+B A •B A B Out 1 1 1 1 1 1 1 A B Out 1 1 1 1 1 A B Out 1 1 1 1 1 1 1 A B Out 1 1 1 1 1 © Mark Redekopp, All rights reserved DeMorgan’s Theorem F = (X+Y) + Z • (Y+W) F = (X+Y) + Z • (Y+W) F = (X+Y) • (Z • (Y+W)) F = (X • Y) • (Z + (Y+W)) F = (X•Y) • (Z + (Y • W)) To find F’, invert both sides of the equation and then use To find F’, invert both sides of the equation and then use DeMorgan’s theorem to simplify… DeMorgan’s theorem to simplify… © Mark Redekopp, All rights reserved Generalized DeMorgan’s Theorem F = (X+Y) + Z • (Y+W) F = X • Y • (Z + (Y • W)) To find F’, swap AND’s and OR’s and complement each To find F’, swap AND’s and OR’s and complement each...
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This note was uploaded on 12/02/2009 for the course EE 101 at USC.
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