Q$4.[4$ points$]$ The state transition table below is for a sequential circuit with one input $\backslash ($ X $\backslash )$ and one output Y$.$ The circuit has two state variables A and B$,$ and asynchronous input Reset that resets the circuit to state $\backslash (\backslash$mathrm$\{$AB$\}=00\backslash )$ when Reset $\backslash (=1\backslash ).$

Complete the given two input$/$output sequences and then determine the function of the circuit. Note the input bits are applied to the circuit from the least significant bit to the most significant. Hint: The circuit is performing an arithmetic function on X$.$