A compact footprint, low-power consumption, and high-speed operation electro-optical full-adder/full-subtractor based on graphene–silicon electro-optical switches is demonstrated. Each switch consists of a Mach–Zehnder interferometer in which few-layer graphene is embedded in a silicon slot waveguide to construct phase shifters. The presented structure can be used as full-adder and full-subtractor simultaneously. The analysis of various factors such as extinction ratio, power consumption, and operation speed has been presented. As will be shown, the proposed electro-optical switch has a minimum extinction ratio of 36.21 dB, maximum insertion loss about 0.18 dB, high operation speed of 180 GHz, and is able to work with a low applied voltage about 1.4 V. Also, the extinction ratio and insertion loss of the full-adder/full-subtractor are about 30 and 1.5 dB, respectively, for transfer electric modes at telecommunication wavelength of 1.55 μm.