CS 3A

 

Computer Science Department Fall Semester 2009
Mathematics, Science and Engineering

 

 



CS 3A
Practice Exercises
(Karnaugh Maps)


1. Write the unsimplified logical expression from the following Karnaugh-map (K-map). Mark each grouping in the K-map. Write the simplest logical expression obtained from the K-map groupings.



2. Fill in the K-map for the expression: X'Y' + XZ' + Y'Z + X'YZ. Mark each grouping in the K-map. Write the simplest logical expression obtained from the K-map groupings.



3. Problem: to design a gate logic circuit to provide an output of 1 (true) when any two or more of the four inputs are 1.

   a) Find the output expression from the truth table.



   b) Build the K-Map for the output from the truth table, and find the simplest logical expression from the K-Map groupings.



   c) Draw the gate circuit for the simplified expression in the following format:



  

Answers:

1. Unsimplified: AB'C'D' + A'BC'D + ABC'D + AB'C'D +ABCD + ABCD'
    Simplified: AB'C' + ABC + BC'D

2. Y' + X'Z + XZ'       (or Y' + (X xor Z))

3. a) Combinations in the truth table that produce a 1 in the output:
                    A'B'CD
                    A'BC'D
                    A'BCD'
                    A'BCD
                    AB'C'D
                    AB'CD'
                    AB'CD
                    ABC'D'
                    ABC'D
                    ABCD'
                    ABCD

   b) The simplest logical expression from the K-map: AB + AC + AD + BC + BD + CD

   c)

  

 

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