Sample Problem:

$($a$)$ Construct a finite state machine that has four states and two possible input values $($a

single input that is either $0$ or $1).$ The state machine should implement a saturating

counter. i$.$e$.$ every input value of $1$ should cause the state machine to go to the next

highest state number $($from $00$ to $01,$ from $01$ to $10,$ from $10$ to $11),$ and for every input

value of $0$ it should go to the next lowest state number $($from $11$ to $10,$ from $10$ to $01,$

from $01$ to $00).$ The state machine should NOT wrap around from $11$ to $00$ or from $00$

to $11-$this is what it means to be a saturating counter: the values saturate at $3$ and $0.$

Show a truth table and resulting FSM$.$ Finish the and$-$or gate array to implement the state

machine. The first row of the and$-$gate array and the first column of the or$-$gate array

have been given. $($Note the numbers of row and column that have been given are different

from that in Homework $2).$