Just a few other things to take in consideration with segment displays..
For multiplexing there are a couple of things to take into account,
By hooking a single resistor in series with the common, you’re going to put every other LED in reverse bias, eg
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If any LED Segment is on (supplied with +5V for example) there will be a voltage potential above the 220ohm resistor, any other LED Segment not in use will now be in reverse bias (reducing the life of each segment)
So the correct way to wire them up would be
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Now the reverse bias is much smaller and the segment will last much longer
Just on multiplexing, NPN's are more efficient for switching common cathode, and PNP's for common anodes. Here’s an example of using an PNP and NPN for a common cathode segment display;
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