Design and implement a register transfer system for the following $6$ micro$-$operations:

: X $$ X $+$ Y $$ NOTE:: this is mathematical plus, not boolean OR$!$

: Y $$ X $$ Y

: X $$ X $$ Y

: Z $$ X NOTE:: the easiest way to implement is: $($X$1)$

: X $$ Y NOTE:: the easiest way to implement is: $(0+$ Y$)$

: X $$ Z$$ NOTE:: this will not be part of the ALU

All registers $($X$,$ Y$,$ and Z$)$ are of $4$ bits.

Complete your register transfer system for the above new register transfers. Test it and demonstrate that it indeed realizes the required register transfers.