CS 2603 Homework 9B — Karnaugh Maps

Due Tuesday, Apr 21, 2015

NOTE: This assignment is due in class at the start of the class period. If you are concerned about being late to class, please turn in your assignment by giving it to me ahead of time during my office hours or by sliding it under my office door if I am not in my office when you turn it in. Do not send assignments to me through email or leave them in my departmental mail box.

1. Motivation

Karnaugh Maps are useful tools for circuit minimization and other logical reductions. To understand them, it is important to gain experience with them.

2. Goal

The goal of this assignment is to give you experience with Karnaugh maps.

3. Assignment

  1. Consider the following Boolean function F.

            a b c d F(a,b,c,d)
            0 0 0 0     0
            0 0 0 1     0
            0 0 1 0     1
            0 0 1 1     0
            0 1 0 0     0
            0 1 0 1     1
            0 1 1 0     0
            0 1 1 1     1
            1 0 0 0     1
            1 0 0 1     0
            1 0 1 0     0
            1 0 1 1     0
            1 1 0 0     0
            1 1 0 1     1
            1 1 1 0     0
            1 1 1 1     1
          
    1. Write the minterms of F as given by the function definition above.
    2. Create a Karnaugh map for F.
    3. Use the Karnaugh map to find a minimum sum-of-products representation of F, give that representation, and show how you arrived at the representation from the map.

  2. Consider the following Boolean function G.

            a b c d G(a,b,c,d)
            0 0 0 0     1
            0 0 0 1     1
            0 0 1 0     0
            0 0 1 1     0
            0 1 0 0     1
            0 1 0 1     1
            0 1 1 0     0
            0 1 1 1     0
            1 0 0 0     0
            1 0 0 1     0
            1 0 1 0     0
            1 0 1 1     0
            1 1 0 0     1
            1 1 0 1     1
            1 1 1 0     0
            1 1 1 1     0
          
    1. Write the minterms of G as given by the function definition above.
    2. Create a Karnaugh map for G.
    3. Use the Karnaugh map to find a minimum sum-of-products representation of G, give that representation, and show how you arrived at the representation from the map.

  3. Consider the following Boolean function H.

            a b c d H(a,b,c,d)
            0 0 0 0     1
            0 0 0 1     1
            0 0 1 0     1
            0 0 1 1     0
            0 1 0 0     0
            0 1 0 1     1
            0 1 1 0     0
            0 1 1 1     0
            1 0 0 0     0
            1 0 0 1     0
            1 0 1 0     1
            1 0 1 1     0
            1 1 0 0     0
            1 1 0 1     1
            1 1 1 0     0
            1 1 1 1     0
          
    1. Write the minterms of H as given by the function definition above.
    2. Create a Karnaugh map for H.
    3. Use the Karnaugh map to find a minimum sum-of-products representation of H, give that representation, and show how you arrived at the representation from the map.

  4. Consider the following Boolean function I.

            a b c d I(a,b,c,d)
            0 0 0 0     1
            0 0 0 1     1
            0 0 1 0     0
            0 0 1 1     0    
            0 1 0 0     x
            0 1 0 1     0
            0 1 1 0     x
            0 1 1 1     1
            1 0 0 0     1
            1 0 0 1     1
            1 0 1 0     0
            1 0 1 1     0
            1 1 0 0     0
            1 1 0 1     0
            1 1 1 0     1
            1 1 1 1     x
          
    1. Write the minterms of I as given by the function definition above.
    2. Create a Karnaugh map for I.
    3. Use the Karnaugh map to find a minimum sum-of-products representation of I, give that representation, and show how you arrived at the representation from the map.

4. Important Notes on this Assignment

  1. Warnings and Cautions

    The following words of advice come directly from Prof Page who has taught this course many times. Please pay them great heed!

    Important Alert! Homework problems provide your only real opportunity to study for exams. Studying the night before the exam will be of almost no use at all. If you have difficulties, come to see the Instructor or Teaching Assistant during office hours.

5. What to Turn In

You will turn in a typed or neatly written hard copy of your homework that shows all the work specified above. You will not need to submit anything electronic for this homework.