A system and method for managing a trail. The distance acquiring section acquires a distance between a user and the image forming apparatus. All teeth detection and signal processing in a short period of time is realized by using a displacement sensor and a high-speed meshing-dedicated circuit board. The device further includes a simplified parity-check unit configured to receive and perform operations on the pre-parity bit, the read-hit bit, and a parity bit from the tag cache memory array, and to output a read-parity bit.