Question 13.15: Product-of-Sums Design Realize the function f described by t...

Known Quantities: Truth table for logic function.

\begin{array}{ccc|c}x & y &z & f \\\hline 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 \\1 & 0 & 1 & 0 \\1 & 1 & 0 & 0 \\1 & 1 & 1 & 0\end{array}

Find: Realization in minimal product-of-sums forms.

Analysis: We cover the Karnaugh map of Figure 13.48 using zeros, and obtain the following function:

f=\bar{z} \cdot(\bar{x}+\bar{y})

Comments: Is the sum-of-products solution simpler? Try it for yourself.