Let's say I have a 'MyDB' SQL Server 2005 database (simple recovery) in which I do a Full backup on Sunday, and Differentials every other night

BACKUP DATABASE [MyDB] TO DISK = N'c:\Database Backups\MyDB\MyDB_Full.bak'
    WITH NOFORMAT, INIT, NAME = N'MyDB.BAK', SKIP, NOREWIND, NOUNLOAD, STATS =
    10

and

BACKUP DATABASE [MyDB] TO DISK = N'c:\Database Backups\MyDB\MyDB_Diff.bak'
    WITH NOINIT, DIFFERENTIAL, NAME= 'MyDB.BAK', STATS= 10

What does the differential backup process use to decide what data gets backed up on the differential nights? Does it need the mydb_full.bak file to do its business?

If I wanted to save disk space, could I zip up the mydb_full.bak file to a .zip file after it's created without adversely affecting the differential backups, and if I needed to restore, just unzip the full backup before starting?