CS 370 – Spring 2004
Introduction to Digital Design
Instructor: Carl Ebeling

Homework Set 2

DISTRIBUTED: April 7
DUE: April 16, Start of class

Collaboration Policy:

Unless otherwise noted, you may collaborate with other CSE370 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 during or immediately after class will incur a 10% penalty. We will penalize your assignment 10% per day for each additional day late.

Please show all of your work. Your solutions must be legible…we will not spend time trying to decipher poorly written assignments.

1. (5 pts) Textbook 2.20

2. (8 pts) Textbook 2.21

3. (12 pts) Textbook 2.23

4. (10 pts) Textbook 2.26: a, c

5. (5 pts) Textbook 2.29: a

6. (10 pts) Show that the NAND gate forms a complete set of gates by showing how AND, OR, and INVERT can each be implemented using only NAND gates.

7. (10 points)

    a) Redraw this circuit using the deMorgan equivalent for gates where appropriate so that the function computed can be read directly from the circuit diagram.
    b) Find the minimal Sum of Products form for this function.
    c) Draw the circuit for this minimal Sum of Products using only NAND gates (and inverters).
    d) Draw the circuit for this minimal Sum of Products using only NOR gates (and inverters).

  8. (15 points)

    a) Translate this circuit directly to a Boolean expression that computes the same function.
    b) Express this function as a canonical Sum of Products.
    c) Express this function as a canonical Product of Sums.
    d) Using a K-map, find the minimal Sum of Products expression for this function.
    e) Using a K-map, find the minimal Product of Sums expression for this function.
    f) Draw the circuit corresponding to the minimal Sum of Products representation.

9. (20 points)  Before you do this problem, you will have to learn how to use the Active-HDL design tools by going through  Tutorial #1 .
Go to the class folder for this homework (\\ntdfs\cs\cse\courses\cse370\04sp\hw2) where you will find a design that you should import into your workspace.  You do this from within Active-HDL by clicking on the Add New File icon, then clicking on the Add Existing File button.  Browse to this folder and choose the hw2.bde file to import.  What you will see is the circuit below.  As you see, the circuit on the left implements the eight minterms for a function of three variables, and the circuit on the right implements the eight maxterms.
    Import the hw2.awf file into your workspace.  This file contains the simulation information for this circuit. Compile the circuit first, select it as the top level and initialize the simulator. Bring up the hw2.awf file.  To run the simulation, first set the simulation run time to 5ns.  Run once to advance time to 5ns.  The inputs should change to 0 0 0.  Now change the simulation run time to 10ns.  Each time you run the simulation now, the inputs should advance to the next value.  (A has been connected to a 3-bit counter stimulator.)
    Implement two different Full Adder circuits, one using a canonical Sum of Products and the other using a canonical Product of Sums.  Create a full adder by adding two OR gates (one which will implement the SUM function and one which will implement the Carry Out function) to the circuit at left.  Then do the same by adding two AND gates to the circuit at right.
    Run the simulation again as described above and watch how the two circuits implement this function.
    Turn in a printout of your circuit schematic (fit to one page please!), and the simulation window.