Question $2[25$ pts$]$

Consider a binary digital combination lock. As shown in Figure below, on its keypad are two number buttons $"0"$ and $"1"$ and a reset button R$.$ The length of the lock code is $6.$ Assume that the code is $101101.$ Whenever the lock detects such an input sequence, it is unlocked. For example, any one of the following binary sequences will unlock it:

$101101$

$0101101$

$011010101101$

$1110001101101101$

At any time, a press on the reset button will take the lock to its initial state. The lock enters its final state when the sequence of the code is detected. Design a state transition diagram for this lock.