The pull-ups and the capacitors

The pull-up gives the line a level

A contact can only connect or not. Closed, it joins its line to GND, and the line is plainly LOW. Open, it connects the line to nothing, and a line connected to nothing is not HIGH: it floats, and reads whatever it picks up.

The 10 kΩ pull-up fixes the open case. It holds the line at VCC while the contact is open, and when the contact closes, the contact wins, because it joins the line to GND with next to no resistance. R4 does this for CLOCK and R3 for DATA. It costs VCC across 10 kΩ while a contact is closed: 0.5 mA from 5 V, 0.33 mA from 3.3 V.

The capacitor slows the rise

C2 on CLOCK and C1 on DATA are 100 nF each, from the line to GND. When a contact closes, it empties its capacitor at once, so the line still falls straight to 0 V. When a contact opens, the line cannot jump back to VCC: the pull-up has to charge the capacitor first, and 10 kΩ × 100 nF is a time constant of 1 ms. The line climbs a little under two-thirds of the way in 1 ms, and passes half of VCC after about 0.7 ms.

Play it with the capacitor fitted, then with 10 kΩ only. The bounce is illustrative: nobody has put this encoder on a scope. The arithmetic is the real RC one.

Bounce, and what the filter does to it

A contact does not close cleanly. It touches, springs apart, and touches again for a short while, and so does it when it opens. Without the capacitor the line follows every one of those, and a sketch that counts falls counts them all. The TK04 push button has the same problem, and the same cause.

With the capacitor, a contact that springs open for a fraction of a millisecond lets the line climb only a small part of the way before it closes again. The line never crosses the switching point, and the pin never sees that bounce. In the figure, three closes become one fall.

What it cannot do

The filter has limits, and they are why the sketches do not rely on it. A bounce that holds the contact open for more than a few tenths of a millisecond can get through as a real HIGH; exactly how long depends on where your chip's input switches. A brief accidental close still pulls the line straight to 0 V, and then it takes the best part of a millisecond to climb back, so the pin sees a LOW. A worn encoder tends to chatter for longer than a new one.

So the filter helps, and the software still has to cope. The last article but one, a state table, is the version that treats any bounce that gets through as a step forward and a step back, which add up to nothing.