Lecture 5: Karnaugh Map Tutorial 3

In the following tutorial, investigate the following: 
  1. the relationship between positions in the truth table and on the Karnaugh map
  2. the relationship between the Karnaugh map and the logic diagram
  3. the relationship between the Karnaugh map and the algebraic expression
  4. the relationship between minterm and maxterm representations of the circuit
Actions: 
  1. clicking on any white area will show the corresponding areas in the other representations
  2. dragging on the Karnaugh map will group terms
  3. double-clicking the logic gate or the algebraic expression will ungroup the terms
  4. an area in pink includes the terms highlighted

In this tutorial we will look at a binary coded decimal to 7 segment decoder. 

 
 
Codes with binary values greater than 9 are not allowed with BCD, so we use don't cares to indicate that such combinations may be either a 0 or a 1. 

You need a Java enabled browser to see the kmapper. 

Questions:

  1. What is the relationship between the ordering in the truth table and the ordering in the Karnaugh map?
  2. What is it about the Karnaugh Map tha makes simplification easier?
  3. Why does the maxterm grouping on the Karnaugh map group the 0s?
  4. The maxterm grouping works by excluding 0s, rather than by including 1s. True or false?
  5. Consider the simplification for the top left segment. Are the simplified minterm and maxterm expressions equivalent? Explain why or why not.
  6. For the top left segment, the  term is included in several minterm groups. Does this matter? Why or why not?
  7. For the minterm representation of a circuit, what is the difference between the OR of AND and the NAND of NAND circuits.
  8. For the maxterm representation of a circuit, what is the difference between the AND of OR and the NOR of NOR circuits.
 
© Donald Bailey, 
Institute of Information Sciences and Technology, 
Massey University