His pieces are most often based simply on mathematical and logical processes, such as tiling, which he attempts to make as clear as possible. His works include: The Four Note Opera, An Hour for Piano, Rational Melodies, the Bonhoeffer Oratorio,Organ and Silence, Riemannoper, and Galileo.
Johnson received the French "Victoires de la Musique" prize for contemporary composition (the French equivalent of the "Grammies") in 2001 for "Kientzy Loops".