(Hardware Description Languages) Write a Verilog module that describes the circuit of Exer...

(Hardware Description Languages) Write a Verilog module that describes the circuit of Exercise 1.

Exercise 1

(Design Problem) Develop a minimized Boolean implementation of a “ones count” circuit that works as follows. The subsystem has four binary inputs: A, B, C, D; and generates a 3-bit output: XYZ. XYZ is 000 if none of the inputs are 1, 001 if one input is 1, 010 if two are one, 011 if three inputs are 1, and 100 if all four inputs are 1.

(a) Draw the truth tables for X, Y, and Z.

---

(b) Minimize the functions X, Y, Z using 4-variable K-maps. Write down the Boolean expressions for the minimized sum-of-products form of each function.

---

(c) Repeat the minimization process, this time deriving product- of-sums form.