SAMPLE

ECE 362 Examination 1

Thursday February 22, 2001
Time 1:00pm to 2:20

Write your answers on these pages. Show all your work. Use backs of pages for scratch work, if needed. Do not separate the pages of this booklet. A 10 point problem should take no more than 6 to 7 minutes. So budget your time accordingly.

1.
a) Give the dual of the following Boolean expression. Do not simplify. Do not remove any original parenthesis, you may add more for clarity.

b) Give the complement of the following Boolean expression. Do not simplify.

2. Prove the following Boolean identity. Use exhaustive proof method. A and B are arbitrary Boolean expressions.

1. A => B iff A+B=B

2. A = B iff (A => B) AND (B => A)

3. We know we can design any Boolean network using only NAND gates. Dr. Egghead has invented a new gate EGG. Prove that any Boolean network can be designed using only EGGs. The function EGG is defined as EGG(x,y)= x'y. You may assume availability of constant logic 1 as an input.

4. For the following Boolean expression obtain the Product-of-Sums expression using Algebraic manipulation.

5. For the following Boolean function f(a, b, c, d), compute the following quantities directly from the Karnaugh Map. Indicate each term on the map.

List of ALL Prime Implicants = ______________________________________

List of Essential Prime Implicants = _____________________________________

Minimal Sum-of-Products = __________________________________________

Minimal Product-of-Sums = _____________________________________

6. For the following Boolean function f(a, b, c, d), give the Reed-Muller Canonical Expression. Reed-Muller: ___________________________________________________

7. For the following Boolean function f(a, b, c, d), give the Reduced BDD for the variable order a,b,c,d.

8. Which of the following operations are used for (a) Quine-McCluskey Tabular method and (b) Iterative Consensus (Tison's) method.

1. Add a new term P if xP and x'P are present.
2. Add a new term PQ if xP and x'Q are present.
3. Add a new term P'Q' if x'P and xQ are present.
4. Put a check against terms xP and x'P when the term P is added.
5. Put a check against terms xP and x'Q when the term PQ is added.
6. Strike out term P when another term Q covers (contains) P.
7. Strike out terms xP and x'Q as soon as the term PQ is added.
8. Strike out terms xP and x'P as soon as the term P is added.

9. For the following multiple output function give the minimal Sum-of-Products and give a two level NAND network implementation. Show all work on Karnaugh maps.

10. For the function f(a,b,c,d) the min-terms are given in the first table. Use the Quine-McCluskey tabular method to generate all Prime Implicants of this function. (Table of Minterms)

11. Write the Petrick function for the following cover table without modifying the table. Simplify the function by Boolean Algebraic manipulation and give one minimal cost cover.

Petrick Function: __________________________________________________

A minimal cost cover: ________________________________________________

12. From the following table of product terms obtain all prime implicants using Tison's consensus method. (Table of Product Terms)

13. Analyze the following circuit for Static Hazards. First generate the 1-sets from the circuit. Then map the one sets on the Karnaugh map. Identify all vector pairs causing Static-1 and Static-0 hazards for this circuit.

14. Trace the wave forms on the following circuit assuming worst case hazard conditions.

15. Generate a test-vector for the node P stuck-at 0 and another test vector for node Q stuck-at 1, using path sensitization method.

16. Generate ALL test-vectors that test the fault node R stuck-at 1. Use Boolean Difference method. Show all algebraic work.