Boolfuck

Boolfuck is an esoteric programming language based on Brainfuck, but operating only on bits. It does, however, provide input and output.

Computational class
Boolfuck can be shown to be Turing-complete by reduction from 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 reduction can be found at the Boolfuck website, listed below.

Differences from Brainfuck

 * Works with bits not bytes (each cell is a single bit)
 * The output character is ; not.
 * The input is read in little endian mode and reads a single bit at a time.
 * Output is stored to a stream, then outputted in little endian mode

Examples
Here is a sample Boolfuck program; it outputs Hello, world!:

+;+;+;+;;+;;+; +;;;;+;+;;+; +;;;+;+;;;+; +;;;;+;+;;+; +;+;;;;+;+;;

External resources

 * Boolfuck website