Question 13.12: Simplifying Expressions by Using Karnaugh Maps Simplify the ...

Known Quantities: f(x, y, z).

Find: Minimal expression for f.

Analysis: We cover a three-term Karnaugh map to reflect the expression give above. The result is shown in Figure 13.42. It is clear that the Karnaugh map can be covered by using just two terms (subcubes): f=x \cdot y+\bar{x} \cdot z. Thus, the term y \cdot z is redundant.

Comments: The Karnaugh map covering clearly shows that the term y \cdot z corresponds to covering a third two-cell subcube vertically intersecting the two horizontal two-cell subcubes already shown. Clearly, the third subcube is redundant.