A Novel Trit-Based Logic Model for Signal Processing and Memory Systems

Traditional binary logic systems have dominated digital computation and signal processing since their inception. However, these systems face growing limitations in expressiveness, fault tolerance, and context-awareness [2]. As digital environments become more dynamic and complex, there is a growing need for computation models that can adapt more intelligently. This paper introduces 3-Level Logic, a novel trinary logic system inspired by the fluid and contextual behavior of biological neurons [4], [16]. The model defines three core logic statesActive (A), Passive (P), and Null (N) as well as a hybrid composite state (X), enabling richer semantic representation, improved noise resilience, and dynamic adaptability [3]. We detail the theoretical framework, including truth tables, ternary logic gates (TAND, TXOR, TOR), waveform representations, and circuit integration strategies [5]. A dedicated memory model is proposed, allowing for logical forgetting, conditional propagation, and parallel recall [11]. Simulations implemented in VB.NET validate the model’s practical effectiveness in signal processing and data compression through demi-nibble encoding [6], [13]. A key innovation of this work is the introduction of Rex, an agent-based logic synthesis engine capable of real-time adaptation [8]. This adaptive layer positions 3-Level Logic as a foundation for intelligent, fault-tolerant, and energy-efficient computing systems.