E15: Fundamentals of Digital Systems - Fall 2015 - HOMEWORK 7

1. Draw a state diagram for this state machine:

2. Create a Moore state machine (i.e. one whose outputs depend on the current state and not directly on the inputs) to recognize the input sequence 010. Your state machine should have a single bit of input X and a single bit of output Y, which is 1 if the last three inputs were 010, and zero otherwise. Note that the input sequence 01010 should cause the output to be 1 twice: once for the second 0 in the input and once for the third 0 in the input.

a. Draw a state diagram for this state machine. Your implementation should have two bits of state for a total of four possible states.

b. Derive the state transition function and the output function from your state diagram.

c. Draw a logic diagram implementing this circuit using two D flip-flops and any additional gates necessary (you may also use MUXes if you like).

3. Create a Verilog implementation and test bench for problem 1 by instantiating two D flip-flops along with two full adders (both contained in the starter code distribution) inside your own module

module hw7_1(clk, rst, X, S);

You may wish to look at the jk_flipflop example to see how to use the D flip-flop module. For the test bench, keep a regular clock with a 20-tick period, and the first positive edge at t = 10. The timing for the X input should be as follows:

Your Verilog simulation should terminate at t " 140.

4. Create a Verilog implementation and test bench for problem 2 using behavioral Verilog (i.e. non-blocking assignments inside of an always block, similar to the example shown in class) to create a module

module hw7_2(clk, rst, X, Y);

For the test bench, keep a regular clock with a 20-tick period, and the first positive edge at t = 10. The timing for the X input should be as follows:

Your Verilog simulation should terminate at t = 220.

Attachment:- homework7.zip