$(4)$ Design a sequential circuit that outputs $2\text{'}$s complement of a bit sequence. The bit sequence will be given to the circuit in reverse order. For instance, if the given bit sequence is $0010101000,$ the circuit should output $1101011000.$

$(5)$ Design a counter that will output $1,2,3,5,8,13$ and repeat again.

$\backslash$table$[[$Number$,$Gray coule$],[0,0,0,0],[1,0,0,1],[2,0,1,1],[3,0,1,0],[4,1,1,0],[5,1,1,1],[6,1,0,1],[7,1,0,0],[3,,,]]$

$(6)$ Gray codes have a useful property in that consecutive numbers differ in only a single bit position.

$($a$)$ Design a $3-$bit modulo $8$ Gray code counter FSM with no inputs and three outputs. $($A modulo $N$ counter counts from $0$ to $N-1,$ then repeats. When reset, the output should be $000.$ On each clock edge, the output should advance to the next Gray code. After reaching $100,$ it should repeat with $000.$

$($b$)$ Extend your modulo $8$ Gray code counter to be an UP$/$DOWN counter by adding an UP input. If UP $=1,$ the counter advances to the next number. If $UP=0,$ the counter retreats to the previous number.