
## Section5.4Exercise

##### 1

Show that Equation (5.3.1) and Equation (5.3.2) represent the same functionality. This shows that the sum of minterms and product of maxterms are complementary.

Solution

The $\sum$ column shows where the sum of minterms evaluates to $1\text{,}$ and the $\prod$ column shows where the product of maxterms evaluates to $0\text{.}$ Of course, in the blank cells the functions evaluate to the complementary value.

 $x$ $y$ $z$ $F(x,y,z) = \sum(0,1,5,6)$ $F(x,y,z) = \prod(2,3,4,7)$ $\binary{0}$ $\binary{0}$ $\binary{0}$ $\binary{1}$ $\binary{0}$ $\binary{0}$ $\binary{1}$ $\binary{1}$ $\binary{0}$ $\binary{1}$ $\binary{0}$ $\binary{0}$ $\binary{0}$ $\binary{1}$ $\binary{1}$ $\binary{0}$ $\binary{1}$ $\binary{0}$ $\binary{0}$ $\binary{0}$ $\binary{1}$ $\binary{0}$ $\binary{1}$ $\binary{1}$ $\binary{1}$ $\binary{1}$ $\binary{0}$ $\binary{1}$ $\binary{1}$ $\binary{1}$ $\binary{1}$ $\binary{0}$