Computational functionalism holds that the mind is a machine that manipulates symbols. Proponents tend to view the brain as a type of Turing machine (Putnam, H. 1960, "Minds and Machines" ). On this view, any device (such as a digital computer) would have a mind by virtue of the operation of the appropriate program.
There is disagreement about whether the nature of the computation is important. Some believe that any Turing machine generating the same outputs from the same inputs as a brain has the same mind. Others argue that internal functioning - the way the calculations are performed - is important so the machine's program would have to work in the same way as the brain in order to instantiate mind.
For a thought-provoking defence of computational functionalism see David Chalmers' article on "minimal computationalism" (http://consc.net/papers/computation.html.)