Note 1: There is a video associated with this repo:
https://www.youtube.com/watch?v=8w09Zy8MQrc
Note 2: The sketches were updated 12/23/2020 to eliminate flicker when the millis() value updates by two. The displays now update every three milliseconds without flicker.
Multiplexing 7-segment displays by segment can eliminate the need for resistors on the segment driver lines, and transistors on the common anode/cathode pins, as required for the traditional multiplexing by digit. All of that is replaced by individual resistors on each CA or CC pin.
Schematics are included here showing the traditional circuit used for multiplexing by digit, and the alternate of multiplexing by segment. A circuit is also shown for the alternate method (for CC displays only) using a 74HC4017 chip to drive the segments to minimize the number of processor pins used for the displays. The number of MCU pins needed with the 4017 setup equals the number of digits, plus one.
Also included are Arduino sketches for the Nano providing demonstration code for both the regular by-segment method and the 4017 method. The sketches have more details on how this all works.
In this method, one segment driver line is turned on at a time, which drives that same segment on all digits. The state of the CA/CC lines determines on which digit(s) that segment lights up. A single resistor on the CA/CC line is sufficient because those lines only source or sink currrent for one segment at a time. However, a segment driver line may need to power its segment on all digits at the same time. That is a limiting factor for this method, but use of high-efficiency low-current displays, such as the Vishay TDSR 1360-IK, may mitigate that problem.
Since each segment is ON only 1/7 of the time, the refresh rate will have to be speeded up so that each segment will be refreshed 40-70 times per second to avoid flicker or shimmer. The included sketches update the display every three milliseconds, which is 333 Hz, or 48 Hz for an individual segment.