As you probably know, that part is obsolete. Analog devices suggests a replacement and if you are doing a new design, I strongly recommend using the new one. At a glance this part has analog & digital inputs.. the digital ones are TTL compatible so almost any micro you pick will work just fine. If you simply need to bit bang the part, use a PIC, CPLD or discrete logic(if it is a small amount). If you need more complicated control, try a microcontroller(pic one based on how much $$ and time involved in using the compiler)..
More programmable logic parts = FPGA, BASIC stamp (Easy to use), Z80 uC from Zilog.. development board & software is $50.. not bad!
The sky is the limit. You just need digital control for that part..
This question is too broad in scope.