Bitwise operation

Hi,

I'm learning to use Postgresql's bitwise operator's as I'm interested
in building super fast search's based on user selections in web forms.

So far so good but I have just lost it a little so I thought I'd post.
Please growl at me if I'm asking on the wrong list :-)

I understand this:

SELECT 111 & 11 = 11

but not this

SELECT 1111 & 111 = 71

I was expecting the second example to be 

SELECT 1111 & 111 = 111

Hmm ...

Maybe I should search on the web for some more info on how to 
understand this logic.
Math was never my strongest I was always better at creative writing.

Any advice much appreciated.
Thanks
Best Regards
Rudi.