Calculate number of states in edge triggered flip flops

Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.

simulate this circuit – Schematic created using CircuitLab

The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of “in” is _.

My question is how can we calculate a number of states in above diagram. Is there any formulae for that or any logic to calculate?

• 2 binary registers. How many combinations they can have? – Eugene Sh. May 31 '18 at 17:31
• only 2 according to that. But if there are 4 combinations then the answer is 4 ? – Himanshu May 31 '18 at 17:33
• How is it 2? Not really. Yes, it is 4. 2^2. BTW, if you look closer, you will identify a 2 bit SISO shift register here. – Eugene Sh. May 31 '18 at 17:33
• If you can explain that supporting your answer. It will be really helpful thanks. – Himanshu May 31 '18 at 17:42
• It can be 00, 01, 10, 11, right? Can you think why it can't be any of these? Can you think of anything else? – Eugene Sh. May 31 '18 at 17:46

Two FFs can be in a total of 22 = 4 states altogether. An appropriate pattern of bits on Input can drive the machine to any given state.