Bitwise operators in SQL

I'm writing SQL code for dynamic page generation in PHP.  I'd like to
be able to determine whether a certain class of users has access to
certain pages.  I was thinking of doing it the usual way: set
bitmasks, e.g. STUDENT=1, INSTRUCTOR=2, STAFF=4, etc., and store
permissions from bitwise AND of applicable masks in the table that
keeps info about each page.  But the problem is that there are no
bitwise operators among Postgres's supported operators.  So, I cannot
write something like

select name from pages where access&2>0;

Is there a standard way to approach this kind of problem?

Many thanks,
--
Arcady Genkin