Complete the following truth table for a $4-$bit shift left$/$right circuit that specifies the number of bits to shift by the $2-$bit word SH and the direction of shift by the $1-$bit $\frac{R}{L}$ signal $(\frac{R}{L}=1$ denotes shift right, $\frac{R}{L}=0$ denotes shift left$).$ Assume the original data is $a0-a3$ and complete the table by assigning which value, $a0-a3,$ should be at each output for each input combination.

$\backslash$table$[[$SH$,$R$/$L$,$f$3,$f$2,$f$1,$f$0],[0,0,0,$a$3,$a$2,$a$1,$a$0],[0,1,0,,,,],[1,0,0,,,,],[1,1,0,,,,],[0,0,1,,,,],[0,1,1,,,,],[1,0,1,,,,],[1,1,1,,,,]]$

a$)$ Are there any redundant cases, and if so which ones?

b$)$ If this were a rotate rather than a shift would you expect redundant cases and if so which ones?