10-bit digital representation with SPDT switches and voltage division
This isn't going to work.  Between the accuracy of your resistors and the accuracy of the A/D, you're not going to get exactly one known reading for each unique switches setting.  Not even close.

In general the way to produce a set of evenly spaced analog values from different switch settings is to do what most D/As do, which is to use a R-2R ladder.  I have to do something else now, so don't have time to get into what a R-2R ladder is, maybe later.  However, this is a well known construct and you will easily find lots about it out there.

Carefully look at your D/A error budget and that of the A/D.  With .1% resistors and depending on the absolute accuracy of the A/D, you might be able to resolve 8 switches if everything works out right.  7 or 6 switches sounds a lot more doable.  10 is definitely in the guaranteed to fail range.