Question 13.17: UsingDon’t Cares to Simplify Expressions—2 Find a minimum pr...
UsingDon’t Cares to Simplify Expressions—2
Find a minimum product-of-sums realization for the expression f(a, b, c).
Known Quantities: Logical expression, don’t care conditions.
Find: Minimal realization.
Schematics, Diagrams, Circuits, and Given Data:
\begin{aligned}&f(a, b, c)=1 \text { for }\{a, b, c\}=\{000,010,011\} \\&f(a, b, c)=\text { don't care for }\{a, b, c\}=\{100,101,110\}\end{aligned}
Analysis: We cover the Karnaugh map of Figure 13.53 using ones, and also using x entries for each don’t care condition. By appropriately selecting two of the three don’t-care entries to be equal to 1 , we complete the covering with one four-cell subcube and one two-cell subcube, to obtain the following minimal expression:
f(a, b, c)=\bar{a} \cdot b+\bar{c}
Comments: Note that we have chosen to set one of the don’t care entries equal to zero, since it would not lead to any further simplification.
