EECS20N: Signals and Systems

Example

Consider the following state machine:

It begins in state a and transitions to state b the first time it encounters a 1 on the input. It then stays in state b arbitrarily long. If it receives a 1 at the input, it must stay in state b. If it receives a 0, then it can either stay in b or transition to a. Given the input sequence

0, 1, 0, 1, 0, 1, ...

then the following are all possible state responses and output sequences:

a, a, b, a, b, a, b, ...
0, 1, 0, 1, 0, 1, ...

a, a, b, b, b, a, b, ...
0, 1, 1, 1, 0, 1, ...

a, a, b, b, b, b, b, ...
0, 1, 1, 1, 1, 1, ...

a, a, b, a, b, b, b, ...
0, 1, 0, 1, 1, 1, ...