# Finite State Machine Minimization

I can't understand how to eliminate the states. I draw this automa and after I create a table of the states (I must minimize it now and after create a minimal table of the states) Is someone who can explain it to me? This is an final state machine (original, not minimizated). In the Paul and Unger diagram I eliminate the equivalent state (are the states that produce the same output). But I see that I done it uncorrectly and I don't know how to proceed. I think that my problem is in process to find the equivalent states.

• There is a step-by-step algorithm. A very simple one. And since you are asking, it is in your textbook. – Eugene Sh. Jul 3 '18 at 18:49
• @EugeneSh. yes. And using it I'm going to eraise all the states, so for me this automa it's already minimal. But it's not so. So I'm asking here – Ciao Jul 3 '18 at 19:01
• Convert alpha to binary (hex is 0~F) – Tony Stewart Sunnyskyguy EE75 Jul 3 '18 at 19:03
• @TonyEErocketscientist I never do this kind of conversion. I must to minimize the Paull and Unger diagram and after create a new table of the states. The new table of the states must be minimale, and there I put an alpha state. Alpha state include all equivalets states. My problem is with the minimization, so I can't delete the equivalet states from the diagram. If I can't do this, so I can't do a minimal table of the states. – Ciao Jul 3 '18 at 19:10
• Then define present & Next states only in table not previous states with same X. Use 0,1 as table entry for next state – Tony Stewart Sunnyskyguy EE75 Jul 3 '18 at 19:20

Welcome to EE.SE! This appears to be a homework question. As such, you need to show us your work so far, and explain which part of the question you're having trouble with. For future reference: Homework questions on EE.SE enjoy/suffer a special treatment. We don't provide complete answers, we only provide hints or Socratic questions, and only when you have demonstrated sufficient effort of your own. Otherwise, we would be doing you a disservice, and getting swamped by homework questions at the same time. See also here.

To minimize a state diagram, you look for states that do the same thing (both next state and outputs) for a given input.

In your state transition table on the left, that means that you are looking for identical rows in the table.

You need to be methodical — it may not be immediately obvious, but states B and F are identical, as are states E and H.

I hope this is enough information to allow you to proceed with the solution.

Note that in your state diagram on the right, you're missing an edge from H to G that's in the table.

• Yess at the end I made it. I do not delet the not equivalent states, but equivalent yes. And in every couple of states I wrote theirs future states and after I delet those future states if thei return to the one of the deleted states. At the end I've got just a couple FB and GE. And using this I can do the minimal table of the states. Alpha state= ADG and Beta state=BEH. I thank all for the help – Ciao Jul 5 '18 at 19:23