Following rules$/$assumptions apply to this system:

$$ The system is driven by an internal clock signal.

$$ The balls are stacked in the storage column with a fixed color and number pattern $(2$

red balls, followed by $3$ green balls, followed by $2$ red balls, followed by $3$ green

balls etc.$)$

$$ Only one ball is released at the time by the mechanical valve.

$$ The mechanical valve is fully manual, meaning there is no circuitry involved. It is

also assumed that the valve cannot be opened again until the previously released ball

passed fully through either channel R or G$,$ was registered by a detector $$ and the

trap door orientation was adjusted.

$$ The detector $$ has internal circuitry to produce a rising edge upon ball passing

through the channels. Therefore, the binary input $$ to your circuit indicates the

presence of a rising edge on the input. Similarly, D indicates absence of a rising edge

on the input.

$$ A trap door is controlled by the circuit output. When the output of the circuit is set to

$0,$ the trap door is opened, allowing the balls to fall through to channel R$.$ Similarly,

when the output of the circuit is $1,$ the trap door is closed, and the balls go into

channel G$.$ Assume the trap door opens and closes instantaneously.

$$ The system is initialized to $=0,$ meaning the trap door is lowered to let balls pass

through to R channel