Homework Set 3 
DUE: Oct 22,1999, 9:30 am

Collaboration Policy:
Unless otherwise noted, you may collaborate with other CSE467 students on the homework assignments. Do not look at homework or exam solutions from previous years. You must spend at least 15 minutes working on a problem before seeking assistance. Collaboration means that you may discuss the problems and make notes during the discussion, but you may not look at other student’s work when writing up your homework. Your homework represents your own work—the homework must show that you understand the material and have worked as an individual on every problem. You may not divide up the task of doing the problem sets in the interpretation of collaboration. You may discuss lecture material with anyone.

Late Homework Policy:
The weekly assignments are due at the beginning of class. Assignments handed in after class will incur a 10% penalty; the penalty will increase by 10% for each additional day late.

Reading:
Review Katz, Chapter 8

Please show all of your work, and remember, your solutions must be legible. The points for each problem are noted on the problem statement.

1. (5 pts) Katz 6.22
 

2. (10 pts) Design a 3-bit counter that counts in the sequence 0, 2, 6, 4, 5, 7, 3, 1. Draw a state transition table, encode the next-state functions (minimizing the logic), and draw circuit schematics for designs using (a) D flip-flops and (b) T flip-flops.
 

3. (10 pts) Katz 8.14. Your state diagram should have 8 states. Also draw a state transition table, encode the next-state functions (minimizing the logic), and draw a circuit schematic for your design using D flip-flops.
 

4. (10 pts) As described in lecture, a one-hot state machine has a flip-flop for each state. This makes designing a one-hot state machine fast and easy—you can read the next-state logic directly off the state diagram or state-transition table. Each next-state function uses only the active predecessor state and the machine input, and there is one product term for each arc of the state diagram.

Implement a vending machine using the one-hot approach. The price of all items is 25¢, and the machine accepts only nickels (5¢), dimes (10¢), and quarters (25¢). Notes:

I. If the buyer inserts too much change, the machine stays in its present state. So for example, if (s)he inserts a quarter after (s)he’s inserted a nickel, the machine stays in the 5¢ state, (s)he does not get any change back, and (s)he doesn’t get the item, either (this machine could go in the HUB…).

II. Assume that your inputs are C₂₅, C₁₀, and C₅ for quarters, dimes, and nickels, respectively, and that your states are M₀, M₅, M₁₀, M₁₅, M₂₀, and M₂₅. Furthermore, assume that coins will be inserted one-at-a-time; thus, only one of C₂₅, C₁₀, and C₅ should be high (or none of them if there is no input) at any given time. All other input combinations are invalid—you may regard them as don’t cares.

III. The machine should automatically reset itself back to the M₀ state after dispensing an item. Assume that the next buyer will not have time to input another coin before the machine resets itself (or if (s)he does, then the machine will eat the coin).
 

Your output, R, releases an item when R = 1; this should happen after the buyer has inserted 25¢. What is the equation for R (hint: this question is very simple)?

Draw a state diagram (assume a Moore machine) and/or a state-transition table, minimize the logic, and draw a circuit diagram for your one-hot state machine. Use D flip-flops and basic logic gates.

5. (5 pts) Calculate the MTBF of the synchronizer shown below, assuming a clock frequency of 25MHz and an asynchronous input with a 1MHz transition rate. Assume that the setup time and propagation delay for the 74ALS74 are both 10ns.