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Digital logic design

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Please explain distributive property on nand nor gates??

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Distrubtive law:  A+ BC = (A+B) + (A+C)  this is the basic formula

NAND GATE : A @ (B @ C) should be equal to (A @ B) @(A @ C)

                        where @ = NAND GATE

A @ (B @ C) = A @(B'+C')

                      = A + BC

(A @ B) @ (A @ C) = (A' + B') @ (A' + C')

                                = AB + AC = A(B + C)

Therefore, A @ (B @ C) != (A @ B) @ (A @ C).

Similarly , apply on NOR gate.

Finally , Distrubutive law is not applicable on  NAND and NOR gates .
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