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Mobile edge computing (MEC) is envisioned as a promising technique to support computation-intensive and timecritical applications in future Internet of Things (IoT) era. However, the uplink transmission performance will be highly impacted by the hostile wireless channel, the low bandwidth, and the low transmission power of IoT devices. Recently, intelligent reflecting surface (IRS) has drawn much attention because of its capability to control the wireless environments so as to enhance the spectrum and energy efficiencies of wireless communications. In this paper, we consider an IRS-aided multidevice MEC system where each IoT device follows the binary offloading policy, i.e., a task has to be computed as a whole either locally or remotely at the edge server. We aim to minimize the total energy consumption of devices by jointly optimizing the binary offloading modes, the CPU frequencies, the offloading powers, the offloading times and the IRS phase shifts for all devices. Two algorithms, which are greedy-based and penalty-based, are proposed to solve the challenging nonconvex and discontinuous problem. It is found that the penalty-based method has only linear complexity with respect to the number of devices, but it performs close to the greedy-based method with cubic complexity with respect to number of devices. Furthermore, binary offloading via IRS indeed saves more energy compared to the case without IRS.