$[10$ points$]$: A scan chain is a common method of testing the functionality of a sequential integrated circuit $($IC$)$ by sending in a stream of data through an input pin $($SCAN$\_$IN$),$ sampling the output from an output pin $($SCAN$\_$OUT$),$ and verifying whether the expected output occurs at each stage. Most chains have a SCAN$\_$ENABLE signal that enables the SCAN$\_$IN data to flow through the scan chain. In this situation, when SCAN$\_$ENABLE is not enabled, the DFlip$-$flops hold their value, and the new input is ignored. The structure of this

$(3)$

$4-$bit scan chain is shown below.