Sequential Circuit --> State Machine Diagram

Discussion in 'Homework Help' started by wazzizit, Jan 14, 2015.

1. wazzizit Thread Starter New Member

Jan 14, 2015
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Hi, I was hoping someone would be able to help me with the question attached. I know the steps to be:
Determine flipflop input equations and output equations; derive next state equation; plot next-state map for each flipflop and outputs; combine these to a state table; plot a state graph. I'm stuck on the first step! All help appreciated!!

Thanks,
A

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2. MikeML AAC Fanatic!

Oct 2, 2009
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I'll get you started: Label the three flip-flops X, Y, Z.

The expression for Dy=~X (read it as NotX).

You write Jx, Kx, Jz and Kz

3. wazzizit Thread Starter New Member

Jan 14, 2015
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Well the output from the AND gate feeds Jx and Kx thus Jx=Kx, but with notX from the Dtype as you said, X and notQ from Z, i'm really struggling to compute what the input equation would be; surly it can't be X.notX.notQ?

4. wazzizit Thread Starter New Member

Jan 14, 2015
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Sorry for the slow reply, I will be more on the ball now!

5. WBahn Moderator

Mar 31, 2012
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As you said, the first step is to determine the flip-flop input equations. You have three flip-flops, two JK and one D, so you have a total of five input equations. What are they? Express each in terms of the outputs of the other flip-flops and/or the inputs to the circuit as a whole.

6. wazzizit Thread Starter New Member

Jan 14, 2015
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Jx=Kx=yQ.X.zQ' and Jz=Kz=yQ.xQ` is four of them and Dy=X' is the other? Where lower case letters are flip-flops and upper case X is the input, and Q represents the output from that block and Q' being Qnot.

7. WBahn Moderator

Mar 31, 2012
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I'd recommend using a consistent nomenclature. You use Jx (signal name followed by FF id) and xQ (FFid followed by signal name). Pick one. Let's use the former since that has the feel of a signal name with a subscript. Also, using upper case X for something that is unrelated to the lower case x can lead to confusion, particular if handwritten since both letters have the same form. But we can deal with that okay.

I agree that Jx=Kx=(X)(Qy)(Qz') but I don't agree with the other two. You day that Dy=X', meaning that the input to the FFy is the inverse of the input signal. See what I mean about using the same letter for two different things? You also need to be more explicit in working out the expression for Jz=Kz. I think you applied DeMorgan's incorrectly.

8. MikeML AAC Fanatic!

Oct 2, 2009
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When I do this, I use lower case x, y, z as subscripts, e.g. for Jx, Dy, etc.

I use upper case X, Y, Z as the Q outputs of the flip-flops. X', Y', Z' or ~X, ~Y, ~Z would be the Q-bar outputs. I suppose you could also use Qx, Qy, Qz and Qx', Qy', and Qz'.

The External input "InputX" is problematic, because we have already said that X is the Q of a ff, so lets call it Ix, which cannot be confused with Jx, Kx, Sx, Rx, etc.

9. wazzizit Thread Starter New Member

Jan 14, 2015
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I'm not sure what I did wrong, this is the only step of the problem that I am having massive difficulties with. My examination is tomorrow and I would be eternally grateful for some guidance as to how to find the input and output equations of FFs from circuit diagrams.

10. WBahn Moderator

Mar 31, 2012
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The input to the Jz and Kz is from the output of a NAND gate, correct?

So that means that Jz and Kz are equal to NOT (A and B) or (A.B)'. If you apply DeMorgan's to this, you get (A'+B')'.