I'm building a small and simple 4-bit CPU and I'm looking for an IC to store the program opcodes. I've considered using eeproms although they seem too large for my purpose, being in the kilobyte range. I was hoping that there was an easy to access memory that stored 8 bit numbers and could be addressed using 4 bit values, or 16 addressable 8 bit values. I would also prefer not to have to purchase an eeprom programmer so that memory could easily be programmed with a micro-controller.
What type of memory IC would be recommended for this purpose?