Sample Test 1 C421                                                                 Name ________________________
Open book, closed notes, closed neighbor

100 points total, use additional paper as needed. Messy/cramped work will be worth fewer points.

1. (20 points) A room has a light in the middle of the ceiling and four light switches, one on each wall. The light will only turn on if an even number of light switches are on.

a. Fill out the truth table for a function Z that describes the behavior of the light.

A B C D | Z__ 
0 0 0 0 | 
0 0 0 1 | 
0 0 1 0 | 
0 0 1 1 | 
0 1 0 0 | 
0 1 0 1 | 
0 1 1 0 | 
0 1 1 1 | 
1 0 0 0 | 
1 0 0 1 | 
1 0 1 0 | 
1 0 1 1 | 
1 1 0 0 | 
1 1 0 1 | 
1 1 1 0 | 
1 1 1 1 | 

a. Give the Sum of Products for Z. DO NOT simplify.

b. Give the minterms in "Little M" notation for Z' (Z complement).

c. Give the Product of Sums expression for Z' (Z complement). DO NOT simplify.

d. Give the maxterms in "Big M" notation.

2. (20 points) A new gate is designed by your company and it is your job to prove that it is universal. The gate's behavior is as follows:

 A B | Z__ 
 0 0 | 1
 0 1 | 0
 1 0 | 1
	  1 1 | 1

  Prove that the gate is universal or explain why it is not.

3. (20 points) Analysis: Draw a circuit diagram (Do Not Simplify) for the following expression: z = (((AB'C)+(A'BC))· (A+B'))' and give the corresponding algebraic expressions for the logic realized at the output of EACH gate. Your expressions should only contain the variables A,B,C and their complements.
 

4. (20 points) Derive a) the truth table, b) simplified expression c) circuit diagram for the following problem.

A three-input majority gate is a gate whose output is 1 whenever a majority of its inputs are 1. Build a circuit using AND/OR/NOT gates that implements the function of the majority gate.

5. (10 points) Give 2 examples of a valid network and 2 examples of an invalid network. Use a minimum of 4 gates per network. NEATLY draw each example.

6. (10 points) Design a CMOS network (using transistors) that implements the function from Question #2 on this exam. Maximum points will be awarded for solutions using as few transistors as possible.