Well the device directly connects the quadrature wheels to the joystick agalog inputs.
Upon reading the joystick values (using successive approximation) the following values are recieved:
15 24 42 33
If these values remind you of grey code, then you are very observant! They correspond to the values 00, 01, 11, 10! Take a look at the mock schematic below and you’ll see that they matche up pretty well with the resistor values.
Here is a PDF for the data sheet for the MC14584 IC.