Digital logic K map question

1. Nov 8, 2015

orangeincup

So I was reading my book and I came across a table, I don't understand how they converted the problem into a table.
They're designing a sequential logic machine and it looks like they made a K map of something, but I don't know what they used. Can anyone explain how the book did this conversion? It doesn't explain anything about it. I understand K maps and truth tables and stuff, but I don't know what they used to create this k-map(if it even is one, I just noticed it said 00, 01, 11, 10 which usually means K map)

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2. Nov 8, 2015

Staff: Mentor

Please remember to always use the formatting template for posts in the homework areas.

This is not a K-map. It's a state transition table. The state changes each time a new input (XY) is clocked into the "machine".

At any given time the machine sits in some state S, and when an input XY is clocked in it changes state according to the associated entry in the table. So for example if the machine was currently in state S2 and XY = 01 was clocked in, the machine would transition to state S3. The Z column represents the output that the machine presents to the world in a given state.

3. Nov 8, 2015

orangeincup

I was going to use the formatting but I don't think there's any equations involved with this(at least that I've used in digital logic), and the question itself is a picture

I understand what a state transition table is and how it works, what I don't know is how they created the table from just the information above

I understand Z is only 1 when the value is a multiple of 4, but how did they know to the actual values inside the table with just the information given?
S0 S1 S2 S3
S1 S2 S3 S2
S2 ...
S3 ...

4. Nov 8, 2015

Staff: Mentor

If XY contains no ones, stay in the same state. If XY contains one one, increase the state by one step number. If XY contains two ones, increase the state by two step numbers. The state reflects the current count of ones.

5. Nov 8, 2015

orangeincup

Oh that makes more sense. Is that something I'm suppose to know for all state machines or is it something specific to this question?

6. Nov 8, 2015

Staff: Mentor

Its the way state machines work in general, so it's important to know.

In a state machine the state itself reflects some "knowledge" of what has transpired in the past, and the machine transitions to new states by some set of rules associated with the current state and some input stimulus. There may be various ways to depict the state table, but they all boil down to a list of "where to go from here" when "something" occurs. The form presented in the problem is pretty economical in that regard.