How to Set Up a State Table for a 2-bit Gray Code Counter?

[gomezfx]

Homework Statement

A counter has two state outputs y1 (the more significant bit) and y2 (the less significant bit) and a control input x. When x = 0, the states of the counter’s flip-flops do not change. When x = 1, the states of the counter’s flip-flops cycle through the codes of a 2-bit Gray code sequence (00 – 01 – 11 – 10) on successive clock pulses.

Homework Equations

The Attempt at a Solution

I am having trouble setting up the state table. The gray code part is what's confusing me I think. Does anyone mind looking at my state table to verify if it's right. Also, how am I supposed to know what the outputs for y1 and y2 yield?

 

[willem2]

Your state table is OK. y1 and y2 just output the current state of the counter, so y1=a and y2 = b