Answer should be option (A).
Option (B) and (C) are clearly wrong. It says: $(\text{input } 11 \implies \text{output }01)$ and $(\text{input } 10 \implies \text{output }00)$, respectively, but, here for every single bit input the output is $2$ bit sequence.
Now, for option (A) we can trace out. Suppose string is $0111$.
at $A$---$0$---> $A$----$1$---> $B$--$1$-->$C$---$1$-->$C$
$O/P$ $00$ $01$ $10$ $10$
We can see here at $(A,0)$---> $(A,00)$ which sum of $0+0=00$, (previous $i/p$ bit $+$ present $i/p$ bit)
$(A,1)$--->$(B,01)$ which is sum of $0+1= 1=01$,
$(B.1)$--->$(C,10)$ which is sum of $1+1=$ (previous $i/p$ bit $+$ present $i/p$ bit)$=10$,
$(C,1)$---> $(C,10)$ which is sum of $1+1=10$
So, answer should be (A).