After choosing state codes, derive next-state and output logic from the state table. With D flip-flops, each D input equals the desired next value of its state bit. Minimize each output column as a Boolean function of the present state and inputs.
Worked example
For a one-bit toggle machine, the table gives Qnext = Q when X = 0 and Qnext = NOT Q when X = 1. Therefore D = Q XOR X. A Moore output indicating the one-state is Y = Q; a Mealy transition pulse could be Y = Q AND X under a separately defined specification.
What to watch for
Keep present-state outputs separate from next-state signals. Similar-looking equations can produce different cycle timing if connected to different points.
Try it yourself
What D equation implements a machine that sets state on X = 1 and otherwise holds?
Answer: D = X OR Q. Once Q becomes one, this rule keeps it one until another control such as reset clears it.
How to study this topic
Begin with named states and a complete transition table. Then choose encodings and derive the logic. Trace inputs over several cycles, checking outputs as well as next states, including reset and unexpected encodings.
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Digital Electronics