This paper investigates the performance of an all-optical logic gate scheme based on a single in-phase and quadrature (I/Q) modulator with direct detection. The proposed scheme of an all-optical logic gate is simple, high speed, and easily reconfigured to realize 24 logic states by adjusting bias voltages, peak-to-peak voltages of the driven RF signals, and the phase shift. As the scheme to realize logic gates is based on the irregular use of a commercially available I/Q modulator and laser source, a specialized logic gate system including a laser, I/Q modulator, and driven RF module should be optimally designed to obtain the best performance. With the system's extinction ratio (ER) and Q-factor as metrics, the performance of the proposed logic gate scheme is analyzed theoretically and numerically in this paper. We first give a new theoretical model of the I/Q modulator. Next, taking the OR gate as an example, the simulations are carried out to analyze performance under the influence of some key factors in the system. Results show that the extinction ratio of the whole system is affected by the phase shift between the two arms of the I/Q modulator and the extinction ratios of two Mach-Zehnder modulators (MZMs), while Q-factor is further influenced by the output power of the laser and the insertion loss of the MZMs in the I/Q modulator. For an I/Q modulator with MZMs having an extinction ratio of 20 dB, the minimum laser output power to obtain a system's ER higher than 16 dB is 3 dBm, while in order to obtain a Q-factor higher than 6, the output power of the laser must not be <10 dBm.