Designing State Diagram for a 2 input sequence detector

Question

For a lab exercise I have to design a 2-input sequence and Im struggling with the state diagram, as It has 2 inputs, i've designed it with one input before. the sequence to be detected is 1032 which can be written as:

\$ A_{0} \text{ | 0 0 1 1} \$
\$ A_{1} \text{ | 1 0 1 0} \$

So how should I go about designing this state diagram?

Answer 1

You need five states:

1. Nothing detected (initial state)
2. Detected 1
3. Detected 10
4. Detected 103
5. Detected 1032

Some hints: Each state has four possible state transitions corresponding to inputs: 00 (0), 01 (2), 10 (3) and 11 (4). Most of these transitions will lead to state one. 01 input will always lead to state two.