When using a common cathode 7-segment display, is there a reason that two resistors can't be used to connect the two cathode pins to GND instead of using seven resistors to connect the seven anode pins to VDD?
I'm assuming there's a good reason, because I haven't been able to find any schematics that do it this way, but I'm unsure of why this would not work?
The purpose of the resistor is to limit current to a segment LED, by dropping the surplus voltage (over the LED Vf) across itself.
When a resistor is used on a common cathode, the current through this resistor would vary by the number of segments lit at any time. Thus, the voltage dropped would change as well. This will lead to intensity of digits changing with number of lit segments.
You can, but you get uneven lighting in good situations, and in worst case, since LEDS (or any given diode) are not perfect systems, variations in them will cause one led to conduct more current then the rest. Eventually it will burn out before the rest, which would lead to the same current to be divided by a smaller amount of imperfect diodes, which would lead to (rinse, lather, repeat).
See Why exactly can't a single resistor be used for many parallel LEDs? for more info.
Each resistor should only be used to control the current through one LED at a time. If on each display one only wanted to drive one segment at a time, one could simply use one resistor to limit current to the display's common wire. This could be a reasonable approach if e.g. one had a ten-digit display and wished to drive it with 1/7 duty cycle. Most of the time, though, one will wish to energize one entire digit at a time, and would thus need one resistor per segment wire.
