Question 1.23: Show that the distributive laws: A·(B+C)=A·B+A·C and A+(B·C)...

Introduction to Digital Electronics [EXP-30805]

Show that the distributive laws:

A·(B+C)=A·B+A·C

and

A+(B·C)=(A+B)·(A+C)

are duals.

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Using the above ‘rule’ of complementing all variables and swapping operators the first equation becomes:

$\overline{A} +(\overline{B} ·\overline{C} )=(\overline{A} +\overline{B} )·(\overline{A} +\overline{C} )$

then letting $\overline{A}=X, \overline{B}=Y, \overline{C}=Z$ gives:

X+(Y·Z)=(X+Y)·(X+Z)

which has the same form as the second equation.

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