explain bits.

This may be very basic, but I am new to this. I was looking in an older Stereo Review magazine (1996 buyers guide) and cd players were either 1 bit, 16 bit, 18 bit or 20 bit, some had dual. I noticed that price did not necessarily determine number of bits, there are expensive 1 bit, and less expensive 20 bit! I have a one bit that is about 5-6 yrs old. I guess I can see 16, 18 or 20 bit as being close, but are there really one bit machines? What do I look for today? do they still make 1 bit machines? Can a 1 bit sound as good as a 20 bit if they are both higher end? Please explain, and thanks.
Rick