Do what Spehro said and use a 10K pot instead of the 1Meg pot. This will
help reduce the amount of flicker but it won't go away.

Why?

When you are right at a transition point between two digital values, the
analog input signal needs to change some tiny amount and you get the higher
value then it goes back to the lower value and so on.  It's called noise.
The infinite analog hisss. Get used to it.

Fortunately for you, there is a simple fix.

It's called hysteresis.

Suppose you have a transition from one count to the next at 1Volt.  This
means that at .99999 volts, one led is on and at 1.0000 volts the next led
is on, so to speak.  Change your code such that it doesn't switch to the
higher led until your input is say, maybe 5% of the way to the next higher
number.  If you sense the input is dropping, don't change to the lower led
until the input has dropped 5% below the threshold. Do you see how this
works? You create a dead-band between input thresholds in your code and get
a flicker free result.

How much hysteresis you use depends on how "noisy" your input signal is and
on what your instructors requirements for accuracy are. (assuming this is a
class project?).  Doesn't matter, real world projects need to deal with
this also.  You get to learn something either way.  In any case, some
analog filtering on the input and some software hysteresis will cure the
problem.

Good luck!
Tom M.

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