Moiré fringes are generated using logical operations on one-bit binary gratings. A traditional moiré effect is observed using the AND operator while an enhanced moiré is observed using the XOR operation. Since the reference grating in this type of moiré is computer generated, fringe shifting to increase sensitivity can be easily accomplished. An alternative scheme, called the average step method, resulting from the logical operations with values averaged over the pitch of the reference grating, can also be used for fractional fringe-order determination. These principles with some applications are demonstrated in this paper.