$12\mathrm{.}34$ Consider the convolutional coder shown in Figure

$12\mathrm{.}24.$ The shift register contents are $S_1{S}_2{S}_3,$ where $S_1$

represents the most recent input. Compute the output se$-$

quence $v_1{v}_2{v}_3$ for $S_1=0$ and for $S_1=1.$ Show that the

two output sequences generated are complements. Is this

desirable? Why?