Question $5.[10$ points$]\backslash (\backslash$Lambda $\backslash$mathrm$\{$SM$\}\backslash )$ chart.

Use an ASM chart to design the following digital system. It has two single$-$bit inputs $\backslash ($ U $\backslash )$ and $\backslash ($ D $\backslash ),$ each coming from a push$-$button, and an $8-$bit output $\backslash ($ C $\backslash ),$ which is initially $0.$ For each press of $\backslash ($ U $\backslash ),$ the system increments $\backslash ($ C $\backslash ).$ For each press of $\backslash ($ D $\backslash ),$ the system decrements $\backslash ($ C $\backslash ).$ If both buttons are pressed, the system does not change $\backslash ($ C $\backslash ).$ The system rolls over: Output $\backslash ($ C $\backslash )$ goes to $0$ after the largest $\backslash ($ C $\backslash )$ when only $\backslash ($ U $\backslash )$ is pressed; and it goes to the largest value of $\backslash ($ C $\backslash )$ after $0$ when only $\backslash ($ D $\backslash )$ is pressed.