Computers in Active Directory

I am new to 2000 Server with Active Directory. I recently added a user to Active Directory but when I went to log into the domain with that user it would not allow me to login. It said that the computer was not a member of the domain. So I went backinto the Active Directory Users and Computers and added the computer name (NETBIOS Name) to Active Directory and then it let me login on that PC. Is this normal for AD? Does the PC have to be added to AD also before you can login on it? Thanks in advance.