Eventually I discovered a useful search term for Google (+oracle +number +xor) and then found out that Oracle has only one logical operator for numbers: BITAND. With BITAND and some math, other operators can be calculated (see also
http://database.itags.org/oracle/22028/[
^])
Hence, the solution is:
Oracle:
UPDATE MyTable SET MyColumn = BITAND(MyColumn, (-1 -256))