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The Problem: Derive the state diagram for a circuit that takes one input, A and gives out one output X, X is to be one, if and only if it detects a sequence "101" in A.

Understanding The problem:

if A=0001011011..

then X=00010010..

Now the first problem is how many states have I got?, for me its two, some of my colleagues argue that they are three. the second question is how many bits do I need for each state, shouldn't they be three? This isn't the whole problem, I should then use flip flops to implement it, but I'm stuck at the state diagram.

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    \$\begingroup\$ What will be the X if A = 1010101 ? \$\endgroup\$
    – across
    Commented Apr 7, 2020 at 20:19
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    \$\begingroup\$ You need either three or four states, depending on whether or not overlapping patterns are allowed. In either case, it only requires 2 FFs to represent 3 or 4 states. \$\endgroup\$
    – Dave Tweed
    Commented Apr 7, 2020 at 20:45

1 Answer 1

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A1, A2 and A3 are shift register outputs (made of 3 D-flip flop) for simplicity. A is your input sequence at IO1, X is your f(A)=seq.101=A1*!A2*A3. table gives all states at every clock rise signal. Key D closed A=1; open A=0. Clock key space close then open to get rise slope. hope this is useful.

enter image description here

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  • \$\begingroup\$ Even though I was more concerned with deriving the state diagram, I find this answer really helpful, thank you. \$\endgroup\$
    – Essam
    Commented Apr 8, 2020 at 5:37

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