Boolfuck
From Esolang
Boolfuck is an esoteric programming language based on Brainfuck, but operating only on bits. It does, however, provide input and output.
[edit] Computational class
Boolfuck can be shown to be Turing-complete by isomorphism with Brainfuck. Each Brainfuck program maps to a Boolfuck program - so anything that can be expressed in Brainfuck can also be expressed in Boolfuck - and Brainfuck is known to be Turing-complete. More details on the isomorphism can be found at the Boolfuck website, listed below.

