In Lab #03, you will design, build, and test a multifunctional logic circuit that implements multiple logic functions. You will be using the Quartus II CAD tool to design the circuit or write VHDL codes. When you have compiled your design, download and test your design on Altera’s DE1 board.
Question 1 Use algebraic manipulation to prove the following Boolean statements.
a) 𝑥𝑥𝑥𝑥 + yz + 𝑥𝑥̅𝑧𝑧 = 𝑥𝑥𝑥𝑥 + 𝑥𝑥̅𝑧𝑧
b) (𝑥𝑥1 + 𝑥𝑥2 + 𝑥𝑥3 + 𝑥𝑥4)(𝑥𝑥1 + 𝑥𝑥2 + 𝑥𝑥3 + 𝑥𝑥̅4) = 𝑥𝑥1 + 𝑥𝑥2 + 𝑥𝑥3
d) (Bonus 10 pts): (𝑥𝑥 + 𝑥𝑥) ∙ (𝑥𝑥 + 𝑧𝑧) ∙ (𝑥𝑥̅ + 𝑧𝑧) = (𝑥𝑥 + 𝑥𝑥) ∙ (𝑥𝑥̅ + 𝑧𝑧)
Question 2 Draw circuits using NMOS transistors to implement each of the functions as shown below.
1) f (x1,x2) = x1 + x2 ;
2) 𝑓𝑓(𝑥𝑥1, 𝑥𝑥2, 𝑥𝑥3 ) = 𝑥𝑥̅1 ∙ 𝑥𝑥̅2 ∙ 𝑥𝑥̅3
3) 𝑓𝑓(𝑥𝑥1, 𝑥𝑥2, 𝑥𝑥3 ) = 𝑥𝑥1 + 𝑥𝑥2 ∙ 𝑥𝑥3 ∙ 𝑥𝑥4 ∙ 𝑥𝑥5
4) 𝑓𝑓(𝑥𝑥1, 𝑥𝑥2, 𝑥𝑥3 ) = 𝑥𝑥1 ∙ 𝑥𝑥2 ∙ 𝑥𝑥3
5) 𝑓𝑓(𝑥𝑥1, 𝑥𝑥2, 𝑥𝑥3, 𝑥𝑥4 ) = 𝑥𝑥̅1 ∙ 𝑥𝑥̅2 ∙ 𝑥𝑥̅3 + 𝑥𝑥̅4 ∙ 𝑥𝑥̅5
