Lecture 5: Karnaugh Map Tutorial 3
In the following tutorial, investigate the
following:
- the relationship between positions in the truth table and on the
Karnaugh
map
- the relationship between the Karnaugh map and the logic diagram
- the relationship between the Karnaugh map and the algebraic
expression
- the relationship between minterm and maxterm representations of
the
circuit
Actions:
- clicking on any white area will show the corresponding areas in
the
other
representations
- dragging on the Karnaugh map will group terms
- double-clicking the logic gate or the algebraic expression will
ungroup
the terms
- 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.
Questions:
- What is the relationship between the ordering in the truth table
and
the
ordering in the Karnaugh map?
- What is it about the Karnaugh Map tha makes simplification easier?
- Why does the maxterm grouping on the Karnaugh map group the 0s?
- The maxterm grouping works by excluding 0s, rather than by
including
1s.
True or false?
- Consider the simplification for the top left segment. Are the
simplified
minterm and maxterm expressions equivalent? Explain why or why not.
- For the top left segment, the
term is included in several minterm groups. Does this matter? Why or
why
not?
- For the minterm representation of a circuit, what is the
difference
between
the OR of AND and the NAND of NAND circuits.
- 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