Why are four states needed with Quadratuer encoders?

[Dave Scheck]

Expanding on what Ken said, and using the encoder wheel he linked to (note that there are many different types of encoder wheels)....

Imagine that you have two sensors , A and B, that are placed on the radius of the encoder such that A is over the inner encoded band and B is over the outer. The way that the encoder wheel is laid out, if sampled properly, A and B will never change states at the same time.

Knowing this, the following table describes the valid state transitions. (assume 0 = dark and 1 = light)

Previous AB     Current AB
     00               01         - Counterclockwise               
     00               10         - Clockwise

     01               11         - Counterclockwise
     01               00         - Clockwise         

     11               10         - Counterclockwise              
     11               01         - Clockwise

     10               00         - Counterclockwise              
     10               11         - Clockwise

Transitions such as 00->11, 01->10, 10->01, 11->00 tell you that there was rotation, but you don't know which direction the rotation was.

So to answer your original question, you have 4 states because there are 4 states that your encoder is reporting.