Consider the following logic circuit whose inputs are functions $${f_1},$$ $${f_2},$$ $${f_3},$$ and output is $$f.$$

Minimum $$SOP$$ for $$f(w, x, y, z)$$ shown in karnaugh $$-$$ map below is

Transform the following logic circuit (without expressing its switching function) into an equivalent logic circuit that employs only $$6$$ $$NAND$$ gates each with $$2$$-inputs.

$$f\left( {A,B} \right) = A' + B$$ Simplified expression for function $$f((x+y,y),z)$$ is