Construct a Moore Circuit for Binary String '01' Detection: Step-by-Step Guide"

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Discussion Overview

The discussion revolves around constructing a Moore machine for detecting the binary sequence '01' in input strings. Participants are exploring the design of the circuit, focusing on the truth table, Karnaugh maps, and the relationship between states and outputs in the context of Moore machines.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in deriving a proper output equation for a Moore machine, noting that the output should not depend on the input.
  • Another participant clarifies that while the next state depends on both the current state and the input, the output should only depend on the current state.
  • A participant suggests that using Karnaugh maps without considering the input leads to an incorrect output equation, proposing to use Karnaugh maps for next states instead.
  • There is a discussion about the output being 1 when in state '01' and 0 otherwise, with some confusion regarding the correct output based on the state diagram.
  • One participant acknowledges a misreading of the output conditions and refers to an external example for clarification.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the correct output conditions for the states in the Moore machine, with some confusion about the application of Karnaugh maps and the relationship between states and outputs. No consensus is reached on the correct output equation.

Contextual Notes

Participants express uncertainty about the application of Karnaugh maps to next states and the implications of the state diagram on output conditions. There are unresolved questions about the correct formulation of the output based on the current state.

DenDanne
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Summary:: I have a problem getting the circuit of the problem to a Moore-solution.

"Construct a Moore Machine and show it in a circuit, that outputs '1' whenever the sequence '01' is encountered in any input binary string (using D-flipflops)".

First of, I have written the Moore Machine.
Untitled.png


I don't think this is where the problem is, as it is quite straight forward in that step.

From this Moore Machine, I do a truth table.
Capture.PNG


And then I use Karnough-diagrams to find equations for A+, B+ and U.
Capture2.PNG

Here is where I get some troubles.
Because by definition of Moore machines. The output shall only be a result of the present state and some output combinatorial logic. NOT the the input. (that is mealy). But as you can see, I get an I in the output formula. So using this method I get an output dependent on the input, which is not allowed!

What have I thought wrong about?
 
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Welcome to PF. :smile:

The next state does depend on the input and the current state, as you have shown. The output only depends on the state, so get rid of the I term in that equation -- it is not used.
 
berkeman said:
Welcome to PF. :smile:

The next state does depend on the input and the current state, as you have shown. The output only depends on the state, so get rid of the I term in that equation -- it is not used.
Thanks!
But if I Karnough without input I, then I get U=A'B. And the problem with this is that there are two times when 01 is the state. Or should I use Karnough on A+ and B+ (next states), that would solve the problem since A+ is only 1 once. But I have never used Karnough on "next states" before.
 
When you are in state 01, the output is 1, and it is 0 otherwise. You have 2 FFs in the circuit, so the combinatorial circuit to generate the output takes the outputs of the two FFs as inputs.

If they are DFFs, the input D terms come from the two K-maps that you have above for the next state.
 
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berkeman said:
When you are in state 01, the output is 1, and it is 0 otherwise. You have 2 FFs in the circuit, so the combinatorial circuit to generate the output takes the outputs of the two FFs as inputs.

If they are DFFs, the input D terms come from the two K-maps that you have above for the next state.
But according the the State Diagram. The output is 0 when I am in state 01? Only in 10 is the output 1. Hence, I'm thinking that U=AB' is correct for U?
 

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