In the last ten years, silicon photonics has made considerable strides in terms of device functionality, performance, and circuit integration for a variety of practical uses, including communication, sensing, and information processing. In this work, we theoretically demonstrate a complete family of all-optical logic gates (AOLGs), including XOR, AND, OR, NOT, NOR, NAND, and XNOR, through finite-difference-time-domain simulations using compact silicon-on-silica optical waveguides that operate at 1.55 μm. Three slots, grouped in the shape of the letter Z, make up the suggested waveguide. The function of the target logic gates is based on constructive and destructive interferences that result from the phase difference experienced by the launched input optical beams. These gates are evaluated against the contrast ratio (CR) by investigating the impact of key operating parameters on this metric. The obtained results indicate that the proposed waveguide can realize AOLGs at a higher speed of 120 Gb/s with better CRs compared to other reported designs. This suggests that AOLGs could be realized in an affordable manner and with improved outcomes to enable the satisfaction of the current and future requirements of lightwave circuits and systems that critically rely on AOLGs as core building elements.