Synthesis of ASCs

1. Devise a state diagram
2. Derive a flow table and reduce states if possible
3. Perform state assignment to get an excitation table
4. Obtain the next-state and output expressions

Circuit Specification

• The system has an input and an output
• When pulses are applied to :
  • The output is equal to if the number of previously applied pulses is even
  • The output is equal to if the number of previously applied pulses is odd

Assume a Moore machine.

Devising a state diagram:

• Let be the state that indicated that an even number of pulses were received
  • State produces output as long as , so it is stable at
• When the next pulse arrives (), we move to the next state which we will call
  • State produces output as long as , so it is stable at
• Next, the pulse ends (), we move to another state
  • State produces output as long as , so it is stable at
• When the next pulse arrives (), we move to another state
  • State produces output as long as , so it is stable at
• When the pulse ends (), we move back to state

State diagram:

Flow table:

Now we need to do some state assignments. If we tried , , , , this would be a bad choice. We know that a transition from to and to in fundamental mode will cause a race condition (bad), since only one variable can change at a time.

Better state assignment: , , , .

We can write:

We arrive at the circuit: