For my 4 Bit computer project, I will need a programmer for the program ROM and the Microcode ROMs as well as other future projects. I do not want to have to buy an expensive programmer when it is only doing the simple task of writing the data and moving the address, so I have decided to make it on an Arduino. There have been multiple projects that have created such a EEPROM programmer but I have selected the design that Ben Eater has made because It seems to be the easiest to edit the design to suit my needs of programming different sizes of EEPROM. It is quite a simple circuit requiring only the Arduino (nano in this case) and two shift registers (74hc595) to provide the extra signals to access all of the address bits.
I plan to give it a ZIF socket to make removing the ROMs easier, giving it 12.5V to be able to program EPROMS as well as putting it on a perfboard to make it more permanent but this will do just fine for now.