Bitmask Flags with Lookup Tables Clarification
I partially agree with Aaron's comment - in the most general case for storing 21 unrelated pieces of information, you'd probably use 21 bit columns.  As a general solution, it may well be your best solution.  If you had multiple bitmask-ed varchar columns, that would translate to a row with possibly over a hundred bit flags. FYI, 21 bits get stored as 3 bytes when you don't define them as NULLable, removing the necessity for space in the NULL bitmap. Since you have multiple bitmask columns, you'd end up with every 8 bits mashed into a byte.

What SQL Server ends up doing with your multi-column queries is eventually a bunch of bitmasking routines (yes! SQL Server uses bitmasks, so they the concept per se can't be all bad!) but for average use cases, it makes life easier for you.

If we had more information about what types of queries you run, we may be able to better advise, because ultimately the use cases dictate the design.

If you persist with the COMPUTED column, I would persist and index it if you haven't already.  It helps some queries, such as


exact matches

WHERE computedInt = POWER(2, 6) -- bit position 7
AND matching on 15th bit and OR matching on 2 other bits (10th and 7th)

WHERE computedInt >= Power(2,14) AND computedInt &lt; Power(2,15)
  AND computedInt &amp; (Power(2,9) + Power(2,6)) > 0


But these are probably exotic samples and yet also real live in some cases.  It's certainly not too much worse than 21 individual bit columns, for which yes your statements could be easier to write, but remember that SQL Server has mashed them for storage into 3 bytes and will be doing the bit-unmasking anyway!  You would have thought if bit-masking were all bad (without exception) then SQL Server wouldn't be doing it, right?

EDIT

Re the scenario of


  Four flags, HasHouse,HasCar,HasCat,HasDog, 0000 is has none, 1111 is has all.


it is more efficient and logically expedient to test all 4 bits at once and do a single integer based operation, e.g.

WHERE computedInt &amp; (POWER(2,10)+POWER(2,5)+POWER(2,3)+POWER(2,1)) = 0 -- has none
WHERE computedInt &amp; (POWER(2,10)+POWER(2,5)+POWER(2,3)+POWER(2,1)) &gt; 0 -- has one or more


Hypothetically, if this were your most exercised query on the table, you might even group the four columns into another computed column and index it separately, making the bitmask unnecessary (just test the resultant int with =0 and &gt;0).  You might even go further and just precompute the answer... horses for courses.