Question

From the logic diagram given below, write the Boolean expression for (1) and (2). Also, derive the Boolean expression (F) and simplify it.

Answer 1

Expression for (1) : (X.Y)'

Expression for (2) : (X+ Y)'

Expression at F : (X.Y)' + (X + Y)'

Simplification of  F(X, Y) = (X.Y)' + (X + Y)'

(X.Y)' + (X + Y)' (Applying De-Morgan's law)

= X' + Y' + X'.Y'

= X' (1 + Y') + Y' (1 + Y' = 1)

= X' + Y'