EE101Lecture6

EE101Lecture6 - Mark Redekopp, All rights reserved...

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Unformatted text preview: Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 6: Logic Simplification Negative Logic 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 + XZ + YZ = XY + XZ T11 (X+Y)(X+Z)(Y+Z) = (X+Y)(X+Z) Mark Redekopp, All rights reserved Logic Simplification Tips Apply DeMorgans to get only literals Factor common subexpressions (use T8/T8), then see if anything reduces or find something of the form of T9-T11 and apply those Remember, single variables in T8-T11 can represent entire sub-expressions in an equation It may be helpful to use T8/T8 to distribute and get the expression in SOP or POS form Replicate terms if needed Mark Redekopp, All rights reserved Simplification F = (X+Y) + Z(Y+Z) + X(Z+Y) = X+Y + ZY+ZZ + XZ +XY (T8 and T8) = X+ Y + YZ+ XZ +XY (T5 and T1) = X+Y(1 + Z + X) + XZ (T8 and T2) 1 = X+Y + XZ (T8 and T2) = (X+X)(X+Z) +Y (T8) = (X+Z)+Y = X + Z +Y (T5 and T1) (Associativity) This doesnt look like it can be simplified further but it can. Mark Redekopp, All rights reserved Negative Logic Recall it is up to us humans to assign meaning to the two voltage levels Thus, far weve used (unknowingly) the positive logic convention where 1 means true and 0 means false In negative logic 0 means true and 1 means false volts time 1=true/on 0=false/off volts time 1=false/off 0=true/on Negative Logic Convention Positive Logic Convention (Value/Meaning) (Value/Meaning) Mark Redekopp, All rights reserved...
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EE101Lecture6 - Mark Redekopp, All rights reserved...

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