The logic systems have $2$ outputs, the output F$1$ is one when the input does not contain $3$ consecutive $1$s in the word $($A$3,$ A$2,$ A$1,$ A$0).$ F$1$ is zero, otherwise. And the output F$2$ is one when the number of logic $1$s in the word $($A$3,$ A$2,$ A$1,$ A$0)$ is odd. The output F$2$ is zero, otherwise.

$1)$ please design and draw this digital system by using PIC$18$F$87$J$11.$

$2)$ please write C program and flowchart to implement the logic system.