Can this shift-register circuit be simplified?
The preferred method for using a NPN or N-MOSFET transistor as a switch is to locate it between the switched device &amp; ground.This method tends to be easier to understand, and much more energy efficient.


Easier for 'on' signals to activate your display, than having to 'think backwards' and 'turn off' every segment you're not using;
Also, think of the power being wasted on heating up your resistors &amp; transistors when shorting (bypassing) LED drive current to ground through the resistor &amp; transistor.


Instead, try using either of these 2 exaple circuits. On the left is an LED being driven by an NPN BJT transistor (like you're already using), and on the right is an LED being driven by an N-channel FET. Notice that, due to the FET's extremely high gate impedance, it does not need a resistor between the shift-register drive pin &amp; itself.