Questions re. Burning Music onto CDs

[F. Hill]

Sometimes maybe I just confuse myself by trying to think things through 
too thoroughly.  Maybe there is a simple answer I am missing.  I have 
lots of old tapes of 1970s radio music.  I want to burn them onto a CD 
to play on a CD player (i.e. not on my computer).  I have figured out 
how to connect my iBook to the tape recorder and I have figured out how 
to record the tapes, or some songs from the tapes, onto my computer.  I 
saved them as .aiff.  Now I am presumably ready to burn them onto a CD.

My question is:  assuming the CD player can read the CD, will the .aiff 
songs play?  Should I convert them to some other format?  And finally, 
what is the mechanism that allows any standard CD player to be able to 
read and play .aiff (or other format) songs? Do CD players have some 
kind of software built into them that can read the music off of CDs?  Or 
am I not understanding things at all?

I know a lot of you guys out there really know this stuff.  I'm trying 
to figure things out and think them through for myself and I am suddenly 
stumped.  What don't I understand?

F. Hill