EE101Lecture7

EE101Lecture7 - Introduction to Digital Logic Lecture 7:...

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© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 7: DeMorgan’s Theorem Logic Simplification Circuit Analysis
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© Mark Redekopp, All rights reserved (X+Y)(X’+Z)(Y+Z) = (X+Y)(X’+Z) T11’ XY + X’Z + YZ = XY + X’Z T11 (X+Y)(X+Y’) = X T10’ XY + XY’ = X T10 X(X+Y) = X T9’ X + XY = X T9 (X+Y)(X+Z) = X+YZ T8’ XY+XZ = X(Y+Z) T8
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© 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 0 1 1 1 0 1 1 1 0 1 0 0 Out B A 0 1 1 0 0 1 0 1 0 1 0 0 Out B A 0 1 1 1 0 1 1 1 0 1 0 0 Out B A 0 1 1 0 0 1 0 1 0 1 0 0 Out B A
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© 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
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This note was uploaded on 02/27/2008 for the course EE 101 taught by Professor Redekopp during the Fall '06 term at USC.

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EE101Lecture7 - Introduction to Digital Logic Lecture 7:...

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