7-Segment Display Wiring and Programming

So would 4 AA or similar batteries in series be a suitable power source? I saw the voltage is typically 6 volts per segment.

That would have a ~3 A current? So then a resistor of roughly 2 Ohm? That can't be right.

So then I have a wire going from each of the segments to the shift register (which pins of the register?). I have one wire going from the Arduino to the shift register. I have a common ground that would connect to the battery, the 7 segment, and the Arduino. Could I get away with a resistor only between the battery and the 7-segment display? Is that how it is connected?