Developments in machine learning and computing power suggest that artificial general intelligence is within reach. This raises the question of artificial consciousness: if a computer were to be functionally equivalent to a human, being able to do all we do, would it experience sights, sounds, and thoughts, as we do when we are conscious? Answering this question in a principled manner can only be done on the basis of a theory of consciousness that is grounded in phenomenology and that states the necessary and sufficient conditions for any system, evolved or engineered, to support subjective experience. Here we employ Integrated Information Theory (IIT), which provides principled tools to determine whether a system is conscious, to what degree, and the content of its experience. We consider pairs of systems constituted of simple Boolean units, one of which -- a basic stored-program computer -- simulates the other with full functional equivalence. By applying the principles of IIT, we demonstrate that (i) two systems can be functionally equivalent without being phenomenally equivalent, and (ii) that this conclusion is not dependent on the simulated system's function. We further demonstrate that, according to IIT, it is possible for a digital computer to simulate our behavior, possibly even by simulating the neurons in our brain, without replicating our experience. This contrasts sharply with computational functionalism, the thesis that performing computations of the right kind is necessary and sufficient for consciousness.