Electronic – Constructing an Encoder

The leftmost column, S, is the current state. The next four columns are for indicating what state you would be in if inputs x and y were to be 00, 01, 10, or 11, respectively. The two right columns are the values of outputs z1 and z2 are for any current state.

Look at the diagram and see that z1 and z2 in the diagram match what z1 and z2 are in the table for any given state.

When you are in State B, you can only transition to one other state, D, and only if input x is a 1. That's what the x next to the arrow going from B to D means in the diagram. If it said x', that means the transition from B to D happens only when x is a 0. Variable y doesn't matter when transitioning from State B to State D.

That is why the first two xy columns are B and the second two are D.

Notice the transitions from State A to State E and from State C to State G. The xy input condition in both of these transitions is when x is 0 AND y is 1. The Boolean function is "not x AND y."

If you don't know Boolean Algebra already, that is somewhat of a prerequisite before approaching more complex state transition diagrams and tables.

I'll give you a hint. Break the inputs into two groups of four. Use a Karnaugh map to give an output when one and only one of four inputs is high. Use another Karnaugh map to create an output that is high when all of the inputs are zero. If you applied 0 through 3 to one of these logic circuits and inputs 4 through 7 to the other logic circuit, can you see how you might combine the outputs of the two logic circuits to give you what you want, at least for four of the inputs?

Now create an exact duplicate of that, but swap the groups of four inputs.

Now you have a big logic circuit with two 1-of-4 logic blocks and two all-0 logic blocks. You can combine the outputs of these blocks to get V.