Confused With Circuit State Diagram and PS/NS Table

Thread Starter


Joined Mar 9, 2007
Hello, I'm doing some studying for my digital circuits class by looking at previous tests, and I've come across a problem that I cant make sense of.

The problem is such:

Theres a few things I dont understand about this.

The first thing is is the PS/NS table. I understand how the y1+ and y2+ outputs were derived from the D Flip Flops, however, the Z output is described as a function of the inputs (Y1 or NOT Y2) which doesnt make sense to me since the inputs get thrown into the Flip-Flops. Shouldnt Z be a function of Y1+ and Y2+?

Secondly in the state diagram, the only variables that seem to be accounted for are Z and X. I don't understand why the inputs Y1 and Y2 are not represented in the diagram and I can't make sense of it.

I would really appreciate some help on this, as I've had no luck so far figuring it out myself. :(


Joined Oct 14, 2005
The real input to the state machine is X only. Y1 and Y2 are the feedback input and are not supplied from outside. This is why only X and Z are accounted for.

You have to appreciate that at any moment in time, there is respectively only one value for Y1 or Y2. The notations Y1+ or Y2+ are there only to show that those will be the next values of Y1 and Y2 after clocking. Thus changing the state of the machine.


Joined Feb 10, 2010
The state table uses a notation that's different from what my professors have been using, we're instructed to put x=0 and x=1 under the NS, thus creating two columns in the NS and PS.
I have a question about the state graph though, I see that it is supposed to be State/Z-output, but if that's the case, why isn't there a logic 1 underneath state 11 and 10 since both have output-Z of 1?