Step 2The "Fader" part.
I cut the diagram down to just show two lights. Keeps it simple to understand. The value of the resistor is one of two factors that will affect the fade time. The other is the Capacitor.
On the output from the counter, there is a standard diode. This keeps the stored up charge in the capacitor from draining back into the counter chip.
The resistor mostly affects the "drain" time. This is how long the LED takes to fade after the signal is cut off. larger values mean more fade, as it takes longer to drain the capacitor, but slightly dimmer light.
The Capacitor mostly affects the "charge" time. When the pulse comes in from the chip, it will start to charge up the capacitor. the LED won't light up, for the most part, until the cap is charged. this leads to a fade-in effect.
Feel free to play with the values. I actually use a different value for each LED.
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