The ACME Company has recently received an order from a Mr$.$ Wiley E$.$ Coyote for their all$-$digital Perfectly Perplexing Padlock. The P$3$ has two buttons $("0"$ and $"1")$ that when pressed cause the FSM controlling the lock to advance to a new state. In addition to advancing the FSM$,$ each button press is encoded on the B signal $($B$=0$ for button $"0",$ B$=1$ for button $"1").$ The padlock unlocks when the FSM sets the UNLOCK output signal to $1,$ which it does whenever the last N button presses correspond to the N$-$digit combination.

Unfortunately, the design notes for the P$3$ are incomplete. Using the specification above and clues gleaned from the partially completed diagrams below fill in the information that is missing from the state transition diagram with its accompanying truth table. When done

each state in the transition diagram should be assigned a $2-$bit state name S$1$S$0($note that in this design the state name is not derived from the combination that opens the lock$),$

the arcs leaving each state should be mutually exclusive and collectively exhaustive,

the value for UNLOCK should be specified for each state, and

the truth table should be completed.

What is the combination for the lock?