I am studying computer architectures in university and my teacher asked me if we can create a computer without PC/IP register?
One possible thought could be a data-flow architecture.
Here the various processing elements are wired together to implement the desired algorithm and rather than an IP register, each processing element (add, subtract, multiply, and, or, compare etc) acts when data is presented.
This sort of things is mostly seen today in fast algorithms embedded in FPGAs. I understand, but have no direct info, that crypto-currency miners are designed along these lines.
So, is this still a computer? Well. oddly enough, a popular way to program these machines uses "C" source code to describe what needs to be done and a sophisticated compiler to design the data-flow machine needed to get the job done.
On a similar note, the LabView programming environment presents a similar model with interconnected elements driven by the data and not an instruction address concept.
It's been done. In some early computers (Bendix G-15 for example) every instruction contained the address of the next instruction.
This odd architectural choice was made because the main memory was a magnetic drum, and reading memory had to wait for the drum to rotate to the correct position. It was important to place the next instruction where it could be read as soon as the current instruction finished execution.