operators and bit field

I haven't seen what operators can be applied to bit masks.

In particular, I am looking to use binary AND:

I want to AND two bitmasks together and see:

A/ if the result has ANY bits set
B/ what bits are set in the results.

SELECT other_fields
FROM some_table
WHERE
( bitmask_8_columnA & bitmask_8_column B) = bitmask_8_patternONE
OR ( bitmask_8_columnA & bitmask_8_column B) = bitmask_8_patternTWO
;

I may try to use a single char for one of the bit masks I need,
is it possible to store all 256 values into a varchar(1) using
escaped input?

Is it possible to AND two varchars within a select and compare the result?

SELECT other_fields
FROM some_table
WHERE ( varchar_1_columnA & varchar_1_columnB ) = 'single_escaped_char_string';