$.(10$ points$)$ Consider the following state table

State X$=0$ X$=1$ Output

S$0$ S$3$ S$10$

S$1$ S$3$ S$10$

S$2$ S$1$ S$50$

S$3$ S$2$ S$60$

S$4$ S$5$ S$41$

S$5$ S$3$ S$21$

S$6$ S$3$ S$40$

Table $1$: Caption

$($a$)$ Using the above state table, group the states by the three assignment guide$-$

lines given in the slides

$($b$)$ Using the assignment groupings in part a$,$ create a $3-$bit state assignment

map and determine optimal state assignments. How many groupings can be

satisfied? How many cannot?

$(10$ points$)$ Consider the following state table

Table $1$: Caption

$($a$)$ Using the above state table, group the states by the three assignment guide$-$

lines given in the slides

$($b$)$ Using the assignment groupings in part a$,$ create a $3-$bit state assignment

map and determine optimal state assignments. How many groupings can be

satisfied? How many cannot?