You people are fantastic! Many thanks for all the help. Not only do you expertly answer the question, but you teach what is needed, to fill the gaps in my tiny little brain.

Specific thanks:
oha - Initial response, understandable "bucket" analogy, non-64-bit algebra example.
syphilis - oha support, great bit-position explanation.
salva - great code example, 64-bit algebra discussion.

You've helped out more than you'll know, and I bow to each of you.

A final bow to the perlmonks site in general, which has created a rose of a website in the abandoned-car-park of the internet.

-Craig