Can I use both C51 and Cx51 to compile the codes for classic 51 chip! And how about the A51 and Ax51.
My understanding was that the CX51 compiler generates code for the MX variant instruction set. I suppose that you could use that code on a classic 8051 if you happened not to generate any MX instructions. But I don't see the benefit to doing so; it's not as though the CX51 compiler has other extra features (as you might expect from the A51 / AX51 or BL51 / LX51 naming schemes). The documentation seems to use the notation Cx51 (or Cx51) to refer to the compilers collectively.
From the horse's mouth: "The CX51 Compiler should only be used to generate code for 51MX derivatives." http://www.keil.com/c51/cx51.htm