$(9$ points$)$ Complete the following problems, which will test your skill in writing RTL statements and identifying implied datapath hardware:

Write valid RTL statements that realize the following transitions. All registers are $1-$bit wide.

If $\backslash$alpha $=1$ THEN copy X to W and copy Z to Y

If $\backslash$alpha $=1$ THEN copy X to W; otherwise copy Z to Y

If $\backslash$alpha $=0$ THEN copy X to W

Show the hardware to implement the RTL statements developed for Part $1.($Your solution should resemble the examples shown in the "Register Transfer Language" lecture notes.$)$

$(21$ points$)$ Assume that all registers are $8$ bits wide and that all operations are $8-$bit operations. Show the hardware components and the needed interconnections to realize the following RTL specification of a digital subsystem. $($Hint: Note the four control signals T$1,$ T$2,\backslash$alpha $,$ and $\backslash$beta $.$ Some of these should be used as multiplexer select inputs, while others should be used as the load inputs of registers R$1$ and R$2.$ Your solution should resemble the examples shown at the end of the "Register Transfer Language" lecture notes.$)$

T$1\backslash$alpha $\text{'}$ : R$1$R$2//$ register copy

T$1\backslash$alpha : R$1$R$1+$ R$2//$ addition

T$2\backslash$beta $\text{'}$ : R$2$R$1//$ register copy

T$2\backslash$beta : R$2$R$1+$ R$2//$ addition