In$-$Class Problem

Find a minimum cost implementation of the following function:

$f(x_1,x_2,x_3)=M(0,4,5,6,7)$

In this situation, cost is defined as the number of logic gates $($ANDs and OR plus the number of gate inputs.

However, complementing the inputs $,$ and $($:$!x_3\}$ is a zero$-$cost operatic meaning do not count the NOT gate and its input for $!x_1,!x_2,$ and $!x_3.$

For example, the cost of $!x_1+x_2$ is $3,1$ OR gate plus $2$ inputs, $!x_1$ and $x_2.$

Hint $1$: You could start by finding the canonical SOP or POS $($whichever is better for this situation$),$ and then, if necessary, use Boolean algebra to simplify further.

Hint $2$: Your final solution should have a cost of $6.$

Module $9$

David O$.$ Johnson EECS $140/141$