detect a change in state of voltage divider without using ADC
To achieve a logic level input using a photoresistor the following must be known:


Resistance of the photoresistor in illuminated and non-illuminated state - Use a multimeter to find out.
GPIO logic level "high" threshold voltage for the microcontroller in question - The datasheet typically provides this.
Assumption: The GPIO is a high-impedance input - Most modern microcontrollers are.


Once the values above are known, a suitable voltage divider will serve as a level-based trigger for the photoresistor. 

To trigger a HIGH if the laser is "tripped", i.e. obscured, this hypothetical photoresistor should be wired on the ground side of the voltage divider, with a fixed resistance on the Vcc side, and the GPIO input pin connected to the junction of these two resistors. 

Here are some assumed values, to illustrate calculations:


Vcc of circuit: 5 Volts
Photoresistor values: 

1 kOhm when illuminated by the laser
1 MOhm when not illuminated

IO port thresholds (from ATmega328 datasheet):

LOW is  &lt; 0.3 Vcc, i.e. &lt; 1.5 Volts
HIGH is > 0.7 Vcc, i.e. > 3.5 Volts
Values in between are not defined, so GPIO could read either way.



If we pick 100 kOhm for the fixed resistor, then the voltage at the junction will be... 


When obscured: 4.55 Volts = HIGH 
When illuminated: 0.495 Volts = LOW


Both values leave sufficient margin for reliable triggering of logic level on the GPIO pin, so required solution is achieved.