We study shift registers in the context of sequential logic circuits. A bidirectional shift register is one in which data can be shifted left or right on the basis of a control input. $($a$)$ Design a $4-$bit bidirectional shift register. Your design should be serial$-$in serial$-$out. Use appropriate labels for all inputs and outputs. $($b$)$ Write an explanation of your design, detailing how it allows data to be shifted and discussing any assumptions. You should use example inputs to illustrate circuit operation. $($c$)$ Outline how your design could be adapted to form an N$-$bit bidirectional shift register that is parallel$-$in parallel$-$out.