How does this "CD4069 smooth bargraph" work?
This circuit relies on the fact that the CD4069, as well as all other &quot;digital&quot; logic ICs, are not really digital but analog electronics operating (usually) at the extremes of saturation and cutoff.  But they can be operated linearly.  Usually this is undesired operation but for an example like this, it can be useful.
The 5 individual inverters are operated as amplifiers in their linear mode until they reach either saturation on the way up or cutoff on the way down.  The resistor in the &quot;ladder&quot; are carefully sized so that the saturation of one corresponds with the start of the linear region of the one above it.
It's easy to just assume that all circuits always behave linearly but they don't.  That's a simplification to make designing digital circuits simpler.