If we have the following Boolean expression: (x.y + z.w)

a) Design a circuit implementing this expression, without simplifying the given expression first. How many logical gates did you use?

b) While using De Morgans Rules, simplify the expression at a) as much as possible. Design a circuit that implements the simplified expression, using AND gates, OR gates and inverters.

c) Derive an implementation for the circuit at b) using only NOR gates and inverters, and create a truth table for the expression of the circuit.