syncing

When you sync it should do a backup or if you like with your phone connected to the computer and itunes on you can right click your phone name in the left column and do a back up that way. You sshould also save a backup of your contacts to you computer another way so tha tyou willever use them. you could use an app like TTvCard and creat a vcf file copy of all you contacts and email it to yourself

Syncing will overwrite your previous backup, it will not transfer anything from the backup to your phone (unless you are restoring from backup). However, the backup only maintains contacts to preserve your favorites and recently called list. This is from Apple:

"Your contacts are part of the backup to preserve recent calls and favorites lists. Back up your contacts to a supported personal information manager (PIM), iCloud, or another cloud-based service to avoid any potential contact data loss." (Reference http://support.apple.com/kb/HT4946).

You should not rely on the backup to archive your contacts; there have been many cases when they were not preserved and users lost their contacts when restoring from a backup. If you can't sync with Outlook or a supported program for contacts then you should sync them with a cloud service (iCloud, Google, Yahoo, etc.) so they are safe.

You're welcome. Also, if you really want a copy of your contacts on your computer as a backup you can use the free app My Contacts Backup to back up your contacts as an attachment to an email. Send this email to yourself and at any point in the future you can open it on your iPhone and tap the attachment to re-import your contact.