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I am supposed to get boolean expressions for the two D-flip flops involved in this state diagram but I am stuck.

I have come up with a truth table (except for output y which I don't understand) for the state diagram but I don't understand how to get the actual expressions of D0 and D1. The hindsight says: D1 = 0, D0 = Q1'Q0'+xQ1Q0+x'Q'0 but I don't know how to get there, I'm struggling with the truth table

How do I do it? This is my truth table based on S0, S1, S2 and S3:

\begin{array}{ccc|ccc} & PS & & & NS \\ D0 & D1 & x & D0 & D1 & y \\ \hline 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 \\ \end{array}

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Consider D0 and D1 as two separate signals, each of which is determined by 3 inputs (D0, D1, and x). Create two separate Karnaugh maps for the two signals, and determine what logic is necessary to create the next value of D0 and D1 given the current state of D0, D1, and x.

As you have observed, it's possible that you end up with trivial logic for some of the bits.

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  • \$\begingroup\$ Thank you. Your answer helped me understand state diagrams. I finally get it! \$\endgroup\$ – Jean Doe Apr 13 at 13:09

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