Lecture 5: Karnaugh Map Tutorial 1

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

You need a Java enabled browser to see the kmapper. 


Note: a 1 input AND gate or a 1 input OR gate is equivalent to a simple connection. 
A 1 input NAND gate or a 1 input NOR gate is equivalent to a NOT. 

Questions:

  1. What is the relationship between the ordering in the truth table and the ordering in the Karnaugh map?
  2. Why can't the minterm expression of the And relation be simplified?
  3. What is the difference between the simplest minterm and maxterm expressions for the And relation?
  4. In the minterm simplification of the Or, does it matter that the A.B term is represented twice? Why or why not?
  5. Why does the maxterm grouping group the 0s?
  6. The maxterm grouping works by excluding 0s, rather than by including 1s. True or false?
  7. Why can the expression for the exclusive or not be simplified?
© Donald Bailey, 
Institute of Information Sciences and Technology, 
Massey University