WARNING! All problems are equally weighted to 10 points out of 200. However, all problems are NOT EQUAL in difficulty or time required! Therefore, to maximize your points, first do problems that you can do easily and in short time.

PROBLEM 1. (10 points)
For the given Boolean function f(a, b, c, d, e), compute the following quantities directly from the 5 variable Karnaugh Map.  Indicate each term on the map.

List of ALL Prime Implicants = ______________________________________
List of Essential Prime Implicants = _____________________________________
A Minimal Sum-of-Products = __________________________________________

Reed-Muller: ___________________________________________________

PROBLEM 4. (10 points)
For the following multiple output function give the minimal PRODUCT-OF-SUMS and give a two level NOR network implementation.

f1 = __________________________________________________________
f2 = __________________________________________________________

Two Level NOR Implementation.

PROBLEM 6. (10 points)
Write the Petrick function for the following cover table without modifying the table. The minterms are: $f(a,b,c,d) = m(....................) and the don't care terms are: d(.....).  Simplify the function by Boolean Algebraic manipulation and give ALL lowest cost covers.

Cover 1: __________________________________________ Cost: ______
Cover 2: __________________________________________ Cost: ______

PROBLEM 8. (10 points)
Generate a test-vector for the node A stuck-at 0 and another test vector for node B stuck-at 1, using path sensitization method.

PROBLEM 9. (10 points)
Given the following function f(a,b,c,d), determine ALL simple disjoint function decompositions that exist of the form f = F(w,x,g(y,z)), (i.e. g is a two variable function).  This problem should be answered directly from the given Karnaugh maps.

PROBLEM 10. (10 points)
Compute the Maximal Set of Permissible Functions (MSPF) for each line in the following network.  Write your answers bit-by-bit directly under the existing function vectors.

PROBLEM 11. (10 points)
Compute the Boolean difference of f(a,b,c,g) with respect to the node g in the following circuit.

PROBLEM 12. (10 points)
You are to analyze the fundamental-mode level-output circuit with the state transition table given below.

Inspect the transition table for essential hazards.  Give your answers in the following tables.

Critical Races:
Encode the states with two bits such that the table is free of any critical race.  Start the encoding with state A=00.

State B:_________       State C:_________        State D:________

Complete the following transition table with your codes and verify that no critical races exist.

Can a finite state machine with one input and one output lines be designed which outputs a 1 iff the input sequence satisfies the
following behavior?

1. The sequence ends in 1111111

Yes/No because_______________________________________________________
 
2. The sequences in which the number of 1's is a power of 2 (i.e. 0,1,2,4,8,16,....).

Yes/No because_______________________________________________________
 
3. The sequences represented by the regular expression (1+0)*

Yes/No because_______________________________________________________
 
4. The sequences in which number of 0's is exactly 3 more than the number of 1's.

Yes/No because_______________________________________________________
 
5. The sequences in which every 1 is immediately followed by an even number of 0's.

Yes/No because_______________________________________________________

PROBLEM 16. (10 points)
Obtain the maximal compatibility classes for the following incompletely specified state table.

PROBLEM 17. (10 points)
Determine a minimum length synchronizing sequence (if one exists) for the following machine.

PROBLEM 18. (10 points)
Find an adaptive homing experiment for the following machine.  Design the experiment so as to minimize the number of inputs that might have to be applied in the worst case.

PROBLEM 19. (10 points)
Find an adaptive distinguishing sequence for the following FSM.

PROBLEM 20. (10 points)
Write a transition diagram starting in state A which recognizes the following regular expression.  Do not simplify.  Lambda's can be left in as is if you use them.
(111+100)* [0001+(110)*]*